Comparing Quantities
Class 7th Mathematics NCERT Exemplar Solution
- 20% of 700 m isA. 560 m B. 70 m C. 210 m D. 140 m
- Gayatri’s income is Rs 1,60,000 per year. She pays 15% of this as house rent and…
- The ratio of Fatima’s income to her savings is 4 : 1. The percentage of money…
- 0.07 is equal toA. 70% B. 7% C. 0.7% D. 0.07%
- In a scout camp, 40% of the scouts were from Gujarat State and 20% of these were…
- What percent of Rs 4500 is Rs 9000?A. 200 B. 1/2 C. 2 D. 50
- 5.2 is equal toA. 52% B. 5.2% C. 520% D. 0.52%
- The ratio 3 : 8 is equal toA. 3.75% B. 37.5% C. 0.375% D. 267%
- 225% is equal toA. 9 : 4 B. 4 : 9 C. 3 : 2 D. 2 : 3
- A bicycle is purchased for Rs 1800 and is sold at a profit of 12%. Its selling…
- A cricket bat was purchased for Rs 800 and was sold for Rs 1600. Then profit…
- A farmer bought a buffalo for Rs 44000 and a cow for Rs 18000. He sold the…
- If Mohan’s income is 25% more than Raman’s income, then Raman’s income is less…
- The interest on Rs 30000 for 3 years at the rate of 15% per annum isA. Rs 4500 B.…
- Amount received on Rs 3000 for 2 years at the rate of 11% per annum isA. Rs 2340…
- Interest on Rs 12000 for 1 month at the rate of 10 % per annum isA. Rs 1200 B. Rs…
- Rajni and Mohini deposited Rs 3000 and Rs 4000 in a company at the rate of 10%…
- If 90% of x is 315 km, then the value of x isA. 325 km B. 350 km C. 405 km D. 340…
- On selling an article for Rs 329, a dealer lost 6%. The cost price of the article…
- 25 % 50 % 100 %/25 x 50 is equal toA. 1.1% B. 0.1% C. 0.01% D. 1%…
- The sum which will earn a simple interest of Rs 126 in 2 years at 14% per annum…
- The per cent that represents the unshaded region in the figure. A. 75% B. 50% C.…
- The per cent that represents the shaded region in the figure is A. 36% B. 64% C.…
- 2 : 3 = ________ % Fill in the blanks to make the statements true.…
- 18 3/4 % = _______ : _______ Fill in the blanks to make the statements true.…
- 30% of Rs 360 = ________. Fill in the blanks to make the statements true.…
- 120 % of 50 km = ________. Fill in the blanks to make the statements true.…
- 2.5 = ________% Fill in the blanks to make the statements true.
- Fill in the blanks: 8/5 = _______ %
- A _______ with its denominator 100 is called a per cent. Fill in the blanks to…
- 15 kg is _______ % of 50 kg. Fill in the blanks to make the statements true.…
- Weight of Nikhil increased from 60 kg to 66 kg. Then, the increase in weight is…
- In a class of 50 students, 8 % were absent on one day. The number of students…
- Savitri obtained 440 marks out of 500 in an examination. She secured _______ %…
- Out of a total deposit of Rs 1500 in her bank account, Abida withdrew 40% of the…
- ________ is 50% more than 60. Fill in the blanks to make the statements true.…
- John sells a bat for Rs 75 and suffers a loss of Rs 8. The cost price of the bat…
- If the price of sugar is decreased by 20%, then the new price of 3kg sugar…
- Mohini bought a cow for Rs 9000 and sold it at a loss of Rs 900. The selling…
- Devangi buys a chair for Rs 700 and sells it for Rs 750. She earns a profit of…
- Sonal bought a bed sheet for Rs 400 and sold it for Rs 440. Her ________% is…
- Nasim bought a pen for Rs 60 and sold it for Rs 54. His ________% is ________.…
- Aahuti purchased a house for Rs 50, 59, 700 and spent Rs 40300 on its repairs. To…
- If 20 lemons are bought for Rs 10 and sold at 5 for three rupees, then ________…
- Narain bought 120 oranges at Rs 4 each. He sold 60 % of the oranges at Rs 5 each…
- A fruit seller purchased 20 kg of apples at Rs 50 per kg. Out of these, 5% of the…
- Interest on Rs 3000 at 10% per annum for a period of 3 years is ________. Fill in…
- Amount obtained by depositing Rs 20,000 at 8 % per annum for six months is…
- Interest on Rs 12500 at 18% per annum for a period of 2 years and 4 months is…
- 25 ml is _________ per cent of 5 litres. Fill in the blanks to make the…
- If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C.…
- Interest = p x r x t/100 where T is ____________ R% is ____________ and P is…
- The difference of interest for 2 years and 3 years on a sum of Rs 2100 at 8% per…
- To convert a fraction into a per cent, we _________ it by 100. Fill in the blanks…
- To convert a decimal into a per cent, we shift the decimal point two places to…
- The _________ of interest on a sum of Rs 2000 at the rate of 6% per annum for 1…
- When converted into percentage, the value of 6.5 is _________ than 100%. Fill in…
- Fill in the blanks so that each mark on the number line is labelled with a per…
- Fill in the blanks so that each mark on the number line is labelled with a per…
- 2/3 = 66 2/3 % State whether the statements are True or False.
- When an improper fraction is converted into percentage then the answer can also…
- 8 hours is 50% of 4 days. State whether the statements are True or False.…
- The interest on Rs 350 at 5% per annum for 73 days is Rs 35. State whether the…
- The simple interest on a sum of Rs P for T years at R% per annum is given by the…
- 75% = 4/3 State whether the statements are True or False.
- 12% of 120 is 100. State whether the statements are True or False.…
- If Ankita obtains 336 marks out of 600, then percentage of marks obtained by her…
- 0.018 is equivalent to 8%. State whether the statements are True or False.…
- 50% of Rs 50 is Rs 25. State whether the statements are True or False.…
- 250 cm is 4% of 1 km.
- Out of 600 students of a school, 126 go for a picnic. The percentage of students…
- By selling a book for Rs 50, a shopkeeper suffers a loss of 10%. The cost price…
- If a chair is bought for Rs 2000 and is sold at a gain of 10%, then selling price…
- If a bicycle was bought for Rs 650 and sold for Rs 585, then the percentage of…
- Sushma sold her watch for Rs 3320 at a gain of Rs 320. For earning a gain of 10%…
- Interest on Rs 1200 for 1 1/2 years at the rate of 15% per annum is Rs 180.…
- Amount received after depositing Rs 800 for a period of 3 years at the rate of…
- Rs 6400 were lent to Feroz and Rashmi at 15% per annum for 3 1/2 and 5 years…
- A vendor purchased 720 lemons at Rs 120 per hundred.10% of the lemons were found…
- Find the value of x if (i) 8% of Rs x is Rs 100 (ii) 32% of x kg is 400 kg (iii)…
- Imagine that a 10 × 10 grid has value 300 and that this value is divided evenly…
- Express 1/6 as a per cent.
- Express 9/40 as a per cent.
- Express 1/100 as a per cent.
- Express 80% as fraction in its lowest term.
- Express 33 1/3 % as a ratio in the lowest term.
- Express 16 2/3 % as a ratio in the lowest form.
- Express 150% as a ratio in the lowest form.
- Sachin and Sanjana are calculating 23% of 800. Now calculate 52% of 700 using…
- Write 0.089 as a per cent.
- Write 1.56 as a per cent.
- What is 15% of 20?
- What is 800% of 800?
- What is 100% of 500?
- What per cent of 1 hour is 30 minutes?
- What per cent of 1 day is 1 minute?
- What per cent of 1 km is 1000 metres?
- Find out 8% of 25 kg.
- What percent of Rs 80 is Rs 100?
- 45% of the population of a town are men and 40% are women. What is the…
- The strength of a school is 2000. If 40 % of the students are girls then how…
- Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon…
- 800 kg of mortar consists of 55% sand, 33% cement and rest lime. What is the…
- In a furniture shop, 24 tables were bought at the rate of Rs 450 per table. The…
- Medha deposited 20% of her money in a bank. After spending 20% of the remainder,…
- The cost of a flower vase got increased by 12%. If the current cost is Rs 896,…
- Radhika borrowed Rs 12000 from her friends. Out of which Rs 4000 were borrowed…
- A man travelled 60 km by car and 240 km by train. Find what per cent of total…
- By selling a chair for Rs 1440, a shopkeeper loses 10%. At what price did he buy…
- Dhruvika invested money for a period from May 2006 to April 2008 at rate of 12%…
- A person wanted to sell a scooter at a loss of 25%. But at the last moment he…
- The population of a village is 8000. Out of these, 80% are literate and of these…
- In an entertainment programme, 250 tickets of Rs 400 and 500 tickets of Rs 100…
- Bhavya earns Rs 50,000 per month and spends 80% of it. Due to pay revision, her…
- In an examination, there are three papers each of 100 marks. A candidate…
- Health Application A doctor reports blood pressure in millimetres of mercury (mm…
- (a) Science Application: The king cobra can reach a length of 558 cm. This is…
- Language Application Given below are few Mathematical terms. Find A. The ratio…
- What’s the Error? An analysis showed that 0.06 per cent of the T-shirts made by…
- What’s the Error? A student said that the ratios 3/4 and 9/16 were proportional.…
- What’s the Error? A clothing store charges Rs 1024 for 4 T-shirts. A student…
- A tea merchant blends two varieties of tea in the ratio of 5 : 4. The cost of…
- A piece of cloth 5 m long shrinks 10 per cent on washing. How long will the…
- Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out…
- A memorial trust donates Rs 5,00,000 to a school, the interest on which is to be…
- Ambika got 99 per cent marks in Mathematics, 76 per cent marks in Hindi, 61 per…
- What sum of money lent out at 16 per cent per annum simple interest would…
- Harish bought a gas-chullah for Rs 900 and later sold it to Archana at a profit…
- Match each of the entries in Column I with the appropriate entries in Column II:…
- In a debate competition, the judges decide that 20 per cent of the total marks…
- Divide Rs 10000 in two parts so that the simple interest on the first part for 4…
- Rs 9000 becomes Rs 18000 at simple interest in 8 years. Find the rate per cent…
- In how many years will the simple interest on a certain sum be 4.05 times the…
- The simple interest on a certain sum for 8 years at 12 per cent per annum is Rs…
- The simple interest on a certain sum for 2.5 years at 12 per cent per annum is…
- Designing a Healthy Diet When you design your healthy diet, you want to make…
- 150 students are studying English, Maths or both. 62 per cent of students study…
- Earth Science: The table lists the world’s 10 largest deserts. A. What are the…
- Geography Application: Earth’s total land area is about 148428950 km^2 . The…
- The pieces of Tangrams have been rearranged to make the given shape. By…
Exercise
Question 1.20% of 700 m is
A. 560 m
B. 70 m
C. 210 m
D. 140 m
Answer:
⇒ 20%(700) = 
= 
= 140m
⇒ Option A is incorrect as 140 m ≠ 560m
⇒ Option B is incorrect as 140 m ≠ 70m
⇒ Option C is incorrect as 140 m ≠ 210m
⇒ Option D is the correct option 140m = 140m
Question 2.
Gayatri’s income is Rs 1,60,000 per year. She pays 15% of this as house rent and 10% of the remainder on her child’s education. The money left with her is
A. Rs 136000
B. Rs 120000
C. Rs 122400
D. Rs 14000
Answer:
Given, Gayatri’s income is 1,60,000 PA
And 15%of1,60,000 = 
= 
= 24000 paid towards rent
And 10%of the remaining is for child’s education
⇒ 160000-24000 = 136000 is the amount left after paying house rent
∴ 10%of 136000 = 
= 13600
⇒ 136000-13600 = 122400 is the amount left after paying rent and child education.
⇒ Option A is incorrect as 136000 ≠ 122400
⇒ Option B is incorrect as 120000 ≠ 122400
⇒ Option C is correct as 122400 = 122400
⇒ Option D is incorrect as 14000 ≠ 122400
Hence, option ‘C’ is the correct one.
Question 3.
The ratio of Fatima’s income to her savings is 4 : 1. The percentage of money saved by her is :
A. 20%
B. 25%
C. 40%
D. 80%
Answer:
Given, the ratio of income to savings of Fatima = 4:1
Need to find out the percentage of money saved by her
⇒ Let the income be 4x and savings be x
⇒ Percentage of money saved by her = 
× 100%
= 
= 
× 100
= 
= 20 %
Hence, the percentage of money saved by her is 20%.
⇒ Option A is the correct one.
⇒ Option B is incorrect as 25% ≠ 20%
⇒ Option C is incorrect as 40% ≠ 20%
⇒ Option D is incorrect as 80% ≠ 20%
Question 4.
0.07 is equal to
A. 70%
B. 7%
C. 0.7%
D. 0.07%
Answer:
Given, 0.07
We need to find out in percentage
∴ 0.07 = 
⇒ the percentage form of can be written as 
Since, to write any number into percent form multiply the given number with %
= 7%
⇒ Option A is incorrect as 70%≠ 7%
⇒ Option B is correct as 7% = 7%
⇒ Option C is incorrect as 0.7%≠ 7%
⇒ Option D is incorrect as 0.07%≠ 7%
Hence, Option B is the correct one.
Question 5.
In a scout camp, 40% of the scouts were from Gujarat State and 20% of these were from Ahmedabad. The percentage of scouts in the camp from Ahmedabad is:
A. 25
B. 32.5
C. 8
D. 50
Answer:
Given, 40% of the scouts were form Gujarat state and 20% of these were from Ahmedabad
Need to find out the percentage of scouts in the camp from Ahmedabad
⇒ Let us consider the scouts in camp be 100
⇒ Then, scouts from Gujarat = 40% of 100 = 
= 40
⇒ Scouts from Ahmedabad = 20% of 40 = 
= 8
∴ Percentage of scouts from Ahmedabad = 
100%
= 
= 8%
⇒ Option A is incorrect as 25%≠ 8%
⇒ Option B is correct as 32.5%≠ 8%
⇒ Option C is correct as 8% = 8%
⇒ Option D is incorrect as 50%≠ 8%
Hence, option C is the correct one
Question 6.
What percent of Rs 4500 is Rs 9000?
A. 200
B. 
C. 2
D. 50
Answer:
Let the percentage be x%
⇒ x% of 4500 = 9000
⇒ 
= 9000
⇒ 45x = 9000
⇒ x% = 
= 200
Hence, option A is the correct one
⇒ Option A is correct as 200 = 200
⇒ Option B is incorrect as 
≠ 200
⇒ Option C is incorrect as 2 ≠ 200
⇒ Option D is incorrect as 50 ≠ 200
Question 7.
5.2 is equal to
A. 52%
B. 5.2%
C. 520%
D. 0.52%
Answer:
Given, 5.2
We need to find out in percentage
∴ 5.2 = 
⇒ the percentage form of can be written as 
Since, to write any number into percent form multiply the given number with %
= 520%
⇒ Option A is incorrect as 5.2 ≠ 520
⇒ Option B is incorrect as 
≠ 520
⇒ Option C is correct as 520 = 520
⇒ Option D is incorrect as 0.50 ≠ 520
Hence, Option C is the correct one.
Question 8.
The ratio 3 : 8 is equal to
A. 3.75%
B. 37.5%
C. 0.375%
D. 267%
Answer:
Given, ratio = 3:8
We need to find out in percentage
∴ 3:8 = 
⇒ the percentage form of
can be written as 
Since, to write any number into percent form multiply the given number with %
= 37.5%
⇒ Option A is incorrect as 3.75 ≠ 37.5
⇒ Option B is correct as 37.5 = 37.5
⇒ Option C is incorrect as 0.375 ≠ 37.5
⇒ Option D is incorrect as 0.267 ≠ 37.5
Hence, Option B is the correct one.
Question 9.
225% is equal to
A. 9 : 4
B. 4 : 9
C. 3 : 2
D. 2 : 3
Answer:
Given, 225%
Need to write it in ratio form
∴ it can be written as 
[ % is removed dividing the given number by 100]
= 
= 
∴ required ratio is 9:4
⇒ Option A is correct as 9:4 = 9:4
⇒ Option B is incorrect as 4:9 ≠ 9:4
⇒ Option C is incorrect as 3:2 ≠ 9:4
⇒ Option D is incorrect as 2:3 ≠ 9:4
Hence, option A is correct one.
Question 10.
A bicycle is purchased for Rs 1800 and is sold at a profit of 12%. Its selling price is
A. Rs 1584
B. Rs 2016
C. Rs 1788
D. Rs 1812
Answer:
Given, cost price of bicycle is 1800 and at 12% profit the bicycle is sold
Need to find out the selling price
⇒ We know that Profit% = 
100
⇒ 12 = 
⇒ Profit = 12 × 18
= 216
∴ SP = CP + Profit = 1800 + 216 = 2016
⇒ the selling price is 2016
⇒ Option A is incorrect as 1584 ≠ 2016
⇒ Option B is correct as 2016 = 2016
⇒ Option C is incorrect as 1788 ≠ 2016
⇒ Option D is incorrect as 1812 ≠ 2016
Hence, option B is the correct one.
Question 11.
A cricket bat was purchased for Rs 800 and was sold for Rs 1600. Then profit earned is
A. 100%
B. 64%
C. 50%
D. 60%
Answer:
Given, cost price of cricket bat = 800 and
Selling price of cricket bat = 1600
Need to find out the profit earned
⇒ Profit = SP-CP
= 1600-800
= 800
⇒ We know that, Profit% = 
× 100%
= 
× 100%
= 100%
∴ profit earned is 100%
⇒ Option A is correct as 100 = 100
⇒ Option B is incorrect as 64 ≠ 100
⇒ Option C is incorrect as 50 ≠ 100
⇒ Option D is incorrect as 60 ≠ 100
Hence, Option A is correct one.
Question 12.
A farmer bought a buffalo for Rs 44000 and a cow for Rs 18000. He sold the buffalo at a loss of 5% but made a profit of 10% on the cow. The net result of the transaction is
A. loss of Rs 200
B. profit of Rs 400
C. loss of Rs 400
D. profit of Rs 200
Answer:
Given, cost price of buffalo is 44000 and cost price of cow is 18000
Buffalo sold at Loss% = 5%
And profit% for cow is 10%
Need to find out the net transaction
⇒ We know that Loss% = 
× 100
⇒ 5 = 
× 100
⇒ Loss = 5 × 440
= 2200
⇒ SP = Cp-loss = 44000-2200
= 41800
⇒ we know that profit% = 10%
⇒ Profit% = 
⇒ 10 = 
× 100
⇒ Profit = 1800
⇒ we know that SP = CP + Profit = 18000 + 1800 = 19800
⇒ total cost of both the animals is 44000 + 18000 = 62000
⇒ Total SP of both the animals is 41800 + 19800 = 61600
Net loss = cp-sp = 62000-61600 = 400
⇒ Option A is incorrect as loss of 200 ≠ loss of 400
⇒ Option B is incorrect as profit of 400 ≠ loss of 400
⇒ Option C is correct as loss of 400
= loss of 400
⇒ Option D is incorrect as profit of 200 ≠ loss of 400
Hence, option C is the correct one.
Question 13.
If Mohan’s income is 25% more than Raman’s income, then Raman’s income is less than Mohan’s income by
A. 25%
B. 80%
C. 20%
D. 75%
Answer:
Given, income of Mohan is 25% more than income of Raman
Need to find out how much less is Raman’s income
⇒ Let, Raman income be x
⇒ Mohan’s income = X + 25% of X
= X + 
X
= X(1 + )
= 
X
⇒ The difference between both the income is X – x
= 
= X
⇒ Raman’s income as compared to Mohan’s income = 
× 100%
= 
× 100%
= 
× 100% = 20%
⇒ Option A is incorrect as 25 ≠20
⇒ Option B is incorrect as 80 ≠ 20
⇒ Option C is correct as 20 = 20
⇒ Option D is incorrect as 75 ≠ 20
Hence, option C is the correct one.
Question 14.
The interest on Rs 30000 for 3 years at the rate of 15% per annum is
A. Rs 4500
B. Rs 9000
C. Rs 18000
D. Rs 13500
Answer:
Given, principal = 30000
Time = 3 years and Rate = 15%
Need to find out the interest
⇒ We know that Interest = 
= 
= 13500
⇒ Option A is incorrect as 4500 ≠ 13500
⇒ Option B is incorrect as 9000 ≠ 13500
⇒ Option C is incorrect as 18000 ≠ 13500
⇒ Option D is correct as 13500 = 13500
Hence, option D is the correct one.
Question 15.
Amount received on Rs 3000 for 2 years at the rate of 11% per annum is
A. Rs 2340
B. Rs 3660
C. Rs 4320
D. Rs 3330
Answer:
Given, principal = 3000
Time = 2 years and Rate = 11%
Need to find out the amount
⇒ we know that amount(A) = P + I
⇒ We know that Interest =
= 
= 660
⇒ Amount = 660 + 3000
= 3660
⇒ Option A is incorrect as 2340 ≠ 3660
⇒ Option B is correct as 3660 = 3660
⇒ Option C is incorrect as 4320 ≠ 3660
⇒ Option D is incorrect as 3330 ≠ 3660
Hence, option B is the correct one.
Question 16.
Interest on Rs 12000 for 1 month at the rate of 10 % per annum is
A. Rs 1200
B. Rs 600
C. Rs 100
D. Rs 12100
Answer:
Given, Principal(P) = 12000
Rate(R) = 10%
Time(T) = 1 month = 
year
Interest = 
= 
= 100
⇒ Option A is incorrect as 1200 ≠ 100
⇒ Option B is incorrect as 600 ≠ 100
⇒ Option C is correct as 100 = 100
⇒ Option D is incorrect as 12100 ≠ 100
Hence, option C is the correct one.
Question 17.
Rajni and Mohini deposited Rs 3000 and
Rs 4000 in a company at the rate of 10% per annum for 3 years and 
years respectively. The difference of the amounts received by them will be
A. Rs 100
B. Rs 1000
C. Rs 900
D. Rs 1100
Answer:
Given, Rajini deposited 3000 and Mohini deposited 4000 in a company
Rate is 10%
Time = 3year and 
years
⇒ we know that amount(A) = P + I
⇒ we know that Interest =
= 
= 900 for rajhini
And for mohini Principal = 4000
Rate = 10%
Time = years = 
I = 
= 1000
⇒ A = 4000 + 1000 = 5000
⇒ Difference of amount = 5000-3900 = 1100
⇒ Option A is incorrect as 100 ≠ 1100
⇒ Option B is incorrect as 1000 = 1100
⇒ Option C is incorrect as 900 ≠ 1100
⇒ Option D is correct as 1100 = 1100
Hence, option D is the correct one.
Question 18.
If 90% of x is 315 km, then the value of x is
A. 325 km
B. 350 km
C. 405 km
D. 340 km
Answer:
Given, 90% of x = 315km
Need to find the value of x
⇒ 
× X = 315
⇒ X = 
⇒ X = 350km
⇒ Option A is incorrect as 325 ≠ 350
⇒ Option B is correct as 350 = 350
⇒ Option C is incorrect as 405 ≠ 350
⇒ Option D is incorrect as 340 ≠ 350
Hence, option B is the correct one.
Question 19.
On selling an article for Rs 329, a dealer lost 6%. The cost price of the article is
A. Rs 310.37
B. Rs 348.74
C. Rs 335
D. Rs 350
Answer:
Given, Selling price = 329 and loss% = 6%
Need to find out the cost price of the article
⇒ We know that Loss% = 
⇒ 6 = 
⇒ 
CP = CP – SP
⇒ CP-CP = 329
⇒ 
CP = 329
⇒ CP = 
CP = 350
⇒ Option A is incorrect as 310.37 ≠ 350
⇒ Option B is incorrect as 348.74 ≠ 350
⇒ Option C is incorrect as 335 ≠ 350
⇒ Option D is correct as 350 = 350
Hence, option D is the correct one.
Question 20.
is equal to
A. 1.1%
B. 0.1%
C. 0.01%
D. 1%
Answer:
⇒ 
= × 
× 
× (
)
= 
× × 1 × 
= 
= 0.0001
In Percentage, 0.0001 × 100% = 0.01%
⇒ Option A is incorrect as 1.1 ≠ 0.01
⇒ Option B is incorrect as 0.1 ≠ 0.01
⇒ Option C is correct as 0.01 = 0.01
⇒ Option D is incorrect as 1 ≠ 0.01
Hence, C is the correct one.
Question 21.
The sum which will earn a simple interest of Rs 126 in 2 years at 14% per annum is
A. Rs 394
B. Rs 395
C. Rs 450
D. Rs 540
Answer:
Given, Interest(I) = 126
Rate = 14%
Time = 2year
⇒ we know that Interest =
⇒ 126 = 
⇒ 12600 = P × 14 × 2
⇒ P = 
= 450
⇒ Option A is incorrect as 394 ≠ 450
⇒ Option B is incorrect as 395 ≠ 450
⇒ Option C is correct as 450 = 450
⇒ Option D is incorrect as 540 ≠ 450
Hence, C is the correct option
Question 22.
The per cent that represents the unshaded region in the figure.
A. 75%
B. 50%
C. 40%
D. 60%
Answer:
Given, total parts = 10 × 10 = 100
Shaded parts = 60
⇒ Percent of shaded parts = 
× 100%
= 60
Then, percent of unshaded parts = 100-60 = 40
∴ unshaded region is 40%
⇒ Option A is incorrect as 75 ≠ 40
⇒ Option B is incorrect as 50 ≠ 40
⇒ Option C is correct as 40 = 40
⇒ Option D is incorrect as 48 ≠ 36
Question 23.
The per cent that represents the shaded region in the figure is
A. 36%
B. 64%
C. 27%
D. 48%
Answer:
Given, total parts = 10 × 10 = 100
Shaded parts = 36
∴ %of shaded parts = 
× 100% = 36%
∴ shaded region is 36%
⇒ Option A is correct as 36 = 36
⇒ Option B is incorrect as 64 ≠ 36
⇒ Option C is incorrect as 27 ≠ 36
⇒ Option D is incorrect as 48 ≠ 36
Hence, the correct option is C.
Question 24.
Fill in the blanks to make the statements true.
2 : 3 = ________ %
Answer:
Given ratio = 2: 3
In percentage = 
= 
Question 25.
Fill in the blanks to make the statements true.
= _______ : _______
Answer:
Given, percentage = 
%
= 
[∵ mixed fraction = 
⇒ 
= 
∴ Ratio = 3:6
Question 26.
Fill in the blanks to make the statements true.
30% of Rs 360 = ________.
Answer:
⇒ 30% of 360 = 
= 108
Question 27.
Fill in the blanks to make the statements true.
120 % of 50 km = ________.
Answer:
⇒ 120% of 50 km = 
= 60km
Question 28.
Fill in the blanks to make the statements true.
2.5 = ________%
Answer:
⇒ 2.5 is written in percentage as 2.5 × 100%
= 250%
Question 29.
Fill in the blanks:
= _______ %
Answer:
⇒ 
is written in percentage as × 100%
= 160%
Question 30.
Fill in the blanks to make the statements true.
A _______ with its denominator 100 is called a per cent.
Answer:
A fraction with its denominator 100 is called a percent.
Question 31.
Fill in the blanks to make the statements true.
15 kg is _______ % of 50 kg.
Answer:
⇒ Let x% of 50 kg be 15kg
⇒ 
= 15
⇒ 
= 15
⇒ x = 15 × 2
⇒ x = 30%
Hence, 15 kg is 30% of 50 kg.
Question 32.
Fill in the blanks to make the statements true.
Weight of Nikhil increased from 60 kg to 66 kg. Then, the increase in weight is _______ %.
Answer:
Given, initial weight of Nikhil = 60kg
After increase in weight, weight became = 66kg
Increase in weight = 66-60 = 6kg
∴ percentage increase = 
= 
× 100%
= 
% = 10%
Question 33.
Fill in the blanks to make the statements true.
In a class of 50 students, 8 % were absent on one day. The number of students present on that day was ________.
Answer:
Given, total number of students = 50
Absent on one day = 8%
⇒ Perecentage of present students on that day = 100-8 = 92%
∴ Number of students present on that day = 92% of 50
= 
× 50
= 
= 46
Hence, the number of students present on that day = 46
Question 34.
Fill in the blanks to make the statements true.
Savitri obtained 440 marks out of 500 in an examination. She secured _______ % marks in the examination.
Answer:
Given, marks obtained by savitri out of 500 = 440
Percentage of marks obtained = 
Hence, savitri secured 88% marks in the examination.
Question 35.
Fill in the blanks to make the statements true.
Out of a total deposit of Rs 1500 in her bank account, Abida withdrew 40% of the deposit. Now the balance in her account is ________.
Answer:
Given, total deposit = Rs. 1500
Amount withdrawn = 40%
⇒ 40% of 1500 = 
= 600
∴ balance in the account = 1500-600
= 900
Question 36.
Fill in the blanks to make the statements true.
________ is 50% more than 60.
Answer:
⇒ Let the number be X.
Given the number X is 50% more than 60
∴ X = 60 + 
= 60 + 30
= 90
Question 37.
Fill in the blanks to make the statements true.
John sells a bat for Rs 75 and suffers a loss of Rs 8. The cost price of the bat is ________.
Answer:
Given, Sp = 75 and Loss = 8
⇒ We know that CP = SP + Loss
= 75 + 8
= 83
∴ CP of the bat is 83
Question 38.
Fill in the blanks to make the statements true.
If the price of sugar is decreased by 20%, then the new price of 3kg sugar originally costing Rs 120 will be ________.
Answer:
Given, price of 3kg sugar = 120
Also the price of sugar is decreased by 20%
∴ new price of sugar = 120 – 20% of original price
= 120 -20% of 120
= 120 – 
= 120 – 24
= 96
Question 39.
Fill in the blanks to make the statements true.
Mohini bought a cow for Rs 9000 and sold it at a loss of Rs 900. The selling price of the cow is ________.
Answer:
Given, CP = 9000 and Loss = 900
⇒ We know that SP = CP –Loss
= 9000-900
= 8100
Hence, the selling price of the cow is 8100
Question 40.
Fill in the blanks to make the statements true.
Devangi buys a chair for Rs 700 and sells it for Rs 750. She earns a profit of ________ % in the transaction.
Answer:
Given, CP of chair = 700 and SP of chair = 750
⇒ we know that, Profit = SP-CP
= 750-700
= 50
Profit% = 
= 
= 
Hence, profit earned by Devangi is
Question 41.
Fill in the blanks to make the statements true.
Sonal bought a bed sheet for Rs 400 and sold it for Rs 440. Her ________% is ________.
Answer:
Given, CP = 400 and SP = 440
⇒ We know that Profit = SP-CP
= 440-400
= 40
And Profit% = 
= 
= 10%
Hence, Sonal’s profit is 10%
Question 42.
Fill in the blanks to make the statements true.
Nasim bought a pen for Rs 60 and sold it for Rs 54. His ________% is ________.
Answer:
Given, CP of a pen = 60 and SP = 54
Loss = CP-SP
= 60-54
= 6
⇒ Loss% = 
= 
= 10%
Question 43.
Fill in the blanks to make the statements true.
Aahuti purchased a house for Rs 50, 59, 700 and spent Rs 40300 on its repairs. To make a profit of 5%, she should sell the house for Rs ________.
Answer:
Given, CP of house = 5059700
And amount spent on repairing = 40300
⇒ Total CP of house = 5059700 + 40300
= 5100000
⇒ Profit% =
⇒ 5 = 
⇒ 5 = 
⇒ 
= SP – 5100000
SP = 5355000
Question 44.
Fill in the blanks to make the statements true.
If 20 lemons are bought for Rs 10 and sold at 5 for three rupees, then ________ in the transaction is ________%.
Answer:
Given, CP of 20 lemons = 10
If SP of 5 lemons = 3
Then SP of 1 lemon = 
∴ SP pf 20 lemons = 
= 12
⇒ Cp = 10 and SP = 12
⇒ Profit = SP-CP = 12 -10
= 2
⇒ We know that Profit% =
= 
= 20%
Question 45.
Fill in the blanks to make the statements true.
Narain bought 120 oranges at Rs 4 each. He sold 60 % of the oranges at Rs 5 each and the remaining at Rs 3.50 each. His _______ is ________%.
Answer:
Given, CP of 1 orange = 4
CP of 120 oranges = 
= 72
∴ SP of 72 oranges = 72 × 5
= 360
And SP of remaining oranges = (120-72) × 3.50
= 48 × 3.50
= 168
∴ Total SP of 120 oranges = 360 + 168
= 528
⇒ We know, that profit% =
= 
= 10%
Question 46.
Fill in the blanks to make the statements true.
A fruit seller purchased 20 kg of apples at Rs 50 per kg. Out of these, 5% of the apples were found to be rotten. If he sells the remaining apples at Rs 60 per kg, then his _________is _________%.
Answer:
Given seller purchased apples at 50 per kg
Total purchased apples = 20kg
⇒ Since, 5% were rotten, so good apples = 20 – 5% of 20kg (rotten)
= 20-
= 20-1
= 19kg
⇒ 19kg apples are sold at 60 per kg
∴ total sp = 19 × 60
= 1140
∴ CP was 20kg apples = 20 × 50 = 1000
∴ Profit = SP-CP = 1140-1000
= 140
⇒ Profit% =
= 
= 
= 14%
Question 47.
Fill in the blanks to make the statements true.
Interest on Rs 3000 at 10% per annum for a period of 3 years is ________.
Answer:
Given, P = 3000
R = 10%
T = 3yr
⇒ we know that I =
=
= 900
Question 48.
Fill in the blanks to make the statements true.
Amount obtained by depositing Rs 20,000 at 8 % per annum for six months is ________.
Answer:
Given, Deposited amount = 20000
Interest = 8%
Time = 6 months = 
year
⇒ we know that I =
= 
= 
= 100 × 8
= 800
∴ amount received = Principal + Interest = 20000 + 800
= 20800
Question 49.
Fill in the blanks to make the statements true.
Interest on Rs 12500 at 18% per annum for a period of 2 years and 4 months is ________.
Answer:
Given, P = 12500 and R = 18%
T = 2yr 4 months
= (2 + 
)year
= (2 + 
= 
year
⇒ we know that I =
= 
= 5250
Question 50.
Fill in the blanks to make the statements true.
25 ml is _________ per cent of 5 litres.
Answer:
⇒ Let 25ml be x% of 5L
⇒ 25ml = x%of5L
⇒ 25 = 
⇒ x = 
⇒ X = 0.5%of 5L
Question 51.
Fill in the blanks to make the statements true.
If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then __________ % of A is equal to C.
Answer:
Given, A is increased by 20% which is equal to B
∴ A + 20% of A = B
⇒ A (1 + 
) = B
⇒ 
A = B
⇒ B = 
A ………….eq1
If B is decreased by 50% then it is equal to C
∴ B-50%of B = C
⇒ B (1-) = C
⇒ B × = C
⇒ B = 2C …………….eq2
⇒ A = 2C
⇒ 
= 
⇒ C = 
∴ C = A
∴ In Percentage, 
= 
× 100%
= × 100%
= 60%
Hence, 60% of A is equal to C
Question 52.
Fill in the blanks to make the statements true.
Interest = 
where
T is ____________
R% is ____________ and
P is ____________.
Answer:
Here, T is time period, R is rate of interest and P is Principal
Question 53.
Fill in the blanks to make the statements true.
The difference of interest for 2 years and 3 years on a sum of Rs 2100 at 8% per annum is _________.
Answer:
Given, P = 2100 and R = 8%
For T = 2Year
⇒ we know that I =
= 
= 336
For 3year
= 
= 504
∴ Difference between both interests = 504 -336 = 168
Question 54.
Fill in the blanks to make the statements true.
To convert a fraction into a per cent, we _________ it by 100.
Answer:
Multiply
Question 55.
Fill in the blanks to make the statements true.
To convert a decimal into a per cent, we shift the decimal point two places to the _________.
Answer:
Right
Question 56.
Fill in the blanks to make the statements true.
The _________ of interest on a sum of
Rs 2000 at the rate of 6% per annum for 
years and 2 years is Rs 420.
Answer:
Given, P = 2000 and R = 6%
For 
year
⇒ we know that I =
= 
= 180
For 2 year
= 
= 240
∴ the sum obtained is 180 + 240 = 420
Question 57.
Fill in the blanks to make the statements true.
When converted into percentage, the value of 6.5 is _________ than 100%.
Answer:
Given, 6.5
In percentage = 6.5 × 100%
= 650%
Question 58.
Fill in the blanks to make the statements true.
Fill in the blanks so that each mark on the number line is labelled with a per cent, a fraction and a decimal. Write all fractions in lowest terms.
Answer:
⇒ Percentage = Fraction × 100
⇒ Fraction = 
⇒ Decimal =
Question 59.
Fill in the blanks to make the statements true.
Fill in the blanks so that each mark on the number line is labelled with a per cent, a fraction and a decimal. Write all fractions in lowest terms.
Answer:
⇒ Percentage = Fraction × 100
⇒ Fraction =
⇒ Decimal =
Question 60.
State whether the statements are True or False.
Answer:
True
Since, = 
%
Question 61.
State whether the statements are True or False.
When an improper fraction is converted into percentage then the answer can also be less than 100.
Answer:
False
Consider, an improper fraction = 
(N >D)
In Percentage, × 100%
= 240%
Question 62.
State whether the statements are True or False.
8 hours is 50% of 4 days.
Answer:
False
⇒ Let 8h be x% of 4 days
⇒ 8h = x% of 4 days
⇒ 8 = 
× 4 × 24
⇒ x = 
= 
Question 63.
State whether the statements are True or False.
The interest on Rs 350 at 5% per annum for 73 days is Rs 35.
Answer:
False
Given, P = 350, R = 5% and T = 73days = 
yr
⇒ I =
= 
= 
= 3.5
Question 64.
State whether the statements are True or False.
The simple interest on a sum of Rs P for T years at R% per annum is given by the formula: Simple Interest 
Answer:
True
SI = 
Question 65.
State whether the statements are True or False.
75% = 
Answer:
False
Given, 75%
⇒ 
= 
⇒ 75% =
Question 66.
State whether the statements are True or False.
12% of 120 is 100.
Answer:
False
Since,12% of 120 = 
× 120 = 
= 14.4
Question 67.
State whether the statements are True or False.
If Ankita obtains 336 marks out of 600, then percentage of marks obtained by her is 33.6.
Answer:
False
Marks obtained by Ankita out of 600 = 336
Percentage, marks = 
× 100% = 56%
Question 68.
State whether the statements are True or False.
0.018 is equivalent to 8%.
Answer:
False
Given, decimal = 0.018
In percentage 0.018 × 100 = 1.8%
Question 69.
State whether the statements are True or False.
50% of Rs 50 is Rs 25.
Answer:
True
Since, 50% of 50 = × 50 = 25
Question 70.
250 cm is 4% of 1 km.
Answer:
False
⇒ 250cm = 
= 2.5m
⇒ Now 4% of 1km = 
× 1000m
= 40m
Question 71.
Out of 600 students of a school, 126 go for a picnic. The percentage of students that did not go for the picnic is 75.
Answer:
False
Total students = 600
Students went for picnic = 126
⇒ Students did not go for picnic = 600-126
= 474
In Percentage, 
× 100% = 79%
Question 72.
By selling a book for Rs 50, a shopkeeper suffers a loss of 10%. The cost price of the book is Rs 60.
Answer:
False
Given, SP = 50 and loss percent = 10%
⇒ Loss% = × 100%
⇒ Loss% = 
× 100
⇒ 10 CP = 100CP –SP×100
⇒ 90CP = 5000
⇒ CP = 
= 55.55
Question 73.
If a chair is bought for Rs 2000 and is sold at a gain of 10%, then selling price of the chair is Rs 2010.
Answer:
False
Given, CP = 2000 and profit% = 10%
⇒ Profit% = × 100
⇒ 10 = 
× 100
⇒ SP-2000 = 200
⇒ Sp = 2200
Question 74.
If a bicycle was bought for Rs 650 and sold for Rs 585, then the percentage of profit is 10.
Answer:
False
Given, CP = 650 and SP = 585
Since, CP > SP
⇒ Loss = CP-SP
= 650-585
= 65
⇒ Loss% =
= 
= 10%
Question 75.
Sushma sold her watch for Rs 3320 at a gain of Rs 320. For earning a gain of 10% she should have sold the watch for Rs 3300.
Answer:
True
Given, SP = 3320 and profit = 320
⇒ CP = SP-Profit = 3320-320 = 3000
⇒ Profit% = × 100%
⇒ 10 = 
× 100
⇒ SP = 3000 + 300
= 3300
Question 76.
Interest on Rs 1200 for years at the rate of 15% per annum is Rs 180.
Answer:
False
Given, P = 1200, T = = 
yr and R = 15%
⇒ I =
= 
= 270
Question 77.
Amount received after depositing Rs 800 for a period of 3 years at the rate of 12% per annum is Rs 896.
Answer:
False
Given, P = 800, T = 3yr and R = 12%
⇒ I =
= 
= 288
⇒ Amount = P + I = 800 + 288
= 1088
Question 78.
Rs 6400 were lent to Feroz and Rashmi at 15% per annum for 
and 5 years respectively. The difference in the interest paid by them is Rs 150.
Answer:
False
Given, Feroz borrowed 6400 for 
yr at 15%
⇒ I1 = 
= 
= 3360
Rashmi borrowed 6400 for 5yr at 15%
I2 = 
= 4800
∴ Difference between interests = 4800-3360 = 1440
Question 79.
A vendor purchased 720 lemons at Rs 120 per hundred.10% of the lemons were found rotten which he sold at Rs 50 per hundred. If he sells the remaining lemons at Rs 125 per hundred, then his profit will be 16%.
Answer:
False
Given, CP of 100 lemons = 120
CP of 1 lemon = 
And CP of 720 lemons = × 720 = 864
⇒ 10% of lemons were rotten
∴ 10%of720 = 
× 720 = 72 lemons
⇒ SP of 100 rotten lemons = 50
⇒ SP of 1 rotten lemon =
And SP of 72 rotten lemons = 
= 36
⇒ SP of 100 good lemons = 125
⇒ SP of 1 good lemon =
And SP of (720-72) good lemons = × (720-72) = × 648 = 810
⇒ Total SP of 720 lemons = 36 + 810 = 846
So, SP < CP
∴ vendor will be loss
Question 80.
Find the value of x if
(i) 8% of Rs x is Rs 100
(ii) 32% of x kg is 400 kg
(iii) 35% of Rs x is Rs 280
(v) 45% of marks x is 405.
Answer:
1) Given, 8% of x = 100
⇒ 
= 100
⇒ X = 1250
2) Given, 32% of x = 400
⇒ 
= 400
⇒ X = 1250
3) Given, 35% of x = 280
⇒ 
= 280
⇒ X = 800
4) Given, 45% of x = 405
⇒ 
= 405
⇒ X = 900
Question 81.
Imagine that a 10 × 10 grid has value 300 and that this value is divided evenly among the small squares. In other words, each small square is worth 3. Use a new grid for each part of this problem, and label each grid “Value : 300.”
A. Shade 25% of the grid. What is 25% of 300? Compare the two answers.
B. What is the value of 25 squares?
C. Shade 17% of the grid. What is 17% of 300? Compare the two answers.
D. What is the value of 
of the grid?
Answer:
A. 
As, Grid contain 100 squares, shade 25 squares in order to shade the 25% of the grid.
Also, value of 1 square = 3
Value of 25 squares = 25 × 3 = 75
and 25% of 300 
∴ Both quantities are equal.
B. Value of 1 square = 3
Value of 25 squares = 25 × 3 = 75
C. 
As, Grid contain 100 squares, Shade 17 squares in order to shade the 17% of the grid.
Also, value of 1 square = 3
Value of 17 squares = 17 × 3 = 51
and 17% of 300 
∴ Both quantities are equal.
D. Value of 1 grid = 300
∴ Value of 
grid 
= 30
Question 82.
Express 
as a per cent.
Answer:
Given, 
In Percentage, × 100% = 
= 16.6%
Question 83.
Express 
as a per cent.
Answer:
Given, 
In Percentage, × 100% = 
%
Question 84.
Express 
as a per cent.
Answer:
Given, 
In Percentage, × 100% = 1%
Question 85.
Express 80% as fraction in its lowest term.
Answer:
Given, 
Fraction, 
= 
= 
Question 86.
Express 
as a ratio in the lowest term.
Answer:
Given, 
For ratio , 
: 1 = 
: 1
= 
:1
= 1:3
Question 87.
Express 
as a ratio in the lowest form.
Answer:
Given, 
= 
For ratio , : 1 = 
: 1
= 
:1
= 1:6
Question 88.
Express 150% as a ratio in the lowest form.
Answer:
Given, 
For ratio , : 1 = 
: 1
= 
:1
= 3:2
Question 89.
Sachin and Sanjana are calculating 23% of 800.
Now calculate 52% of 700 using both the ways described above. Which way do you find easier?
Answer:
First way
⇒ 52% of 700 = (1% of 700) × 52
= (
× 52
= 0.01 × 700 × 52
= 7 × 52
= 364
Second way
⇒ 52% of 700 = 
× 700
= 0.52 × 700
= 364
∴ second way is easier
Question 90.
Write 0.089 as a per cent.
Answer:
Given, 0.089
In Percentage, 0.089 × 100% = 8.9%
Question 91.
Write 1.56 as a per cent.
Answer:
Given, 1.56
In Percentage, 1.56 × 100% = 156%
Question 92.
What is 15% of 20?
Answer:
Given, 15% of 20
= 
× 20 = 3
Question 93.
What is 800% of 800?
Answer:
Given, 800% of 800
= 
× 800 = 6400
Question 94.
What is 100% of 500?
Answer:
Given, 100% of 500
= × 500 = 500
Question 95.
What per cent of 1 hour is 30 minutes?
Answer:
⇒ Let x% of 1h be 30 min
⇒ × 1h = 30min
⇒ × 60min = 30min
⇒ x = 
⇒ X = 50%
Question 96.
What per cent of 1 day is 1 minute?
Answer:
⇒ Let x% of 1day be 1 min
⇒ × 1day = 1min
⇒ × 24h = 1min
⇒ × 1440min = 1min
⇒ x = 
⇒ X = 0.069%
Question 97.
What per cent of 1 km is 1000 metres?
Answer:
⇒ Let x% of 1km be 1000 m
⇒ × 1km = 1000m
⇒ × 1000m = 1000m
⇒ x = 100%
Question 98.
Find out 8% of 25 kg.
Answer:
⇒ 8% of 25 = 
× 25 = 2kg
Question 99.
What percent of Rs 80 is Rs 100?
Answer:
⇒ Let x% of 80 be 100
⇒ × 80 = 100
⇒ x = 125%
Question 100.
45% of the population of a town are men and 40% are women. What is the percentage of children?
Answer:
Given, percentage of men in town = 45%
And women = 40%
∴ percentage of children = 100-45-40 = 15%
Question 101.
The strength of a school is 2000. If 40 % of the students are girls then how many boys are there in the school?
Answer:
Given, the strength of school = 2000
percentage of girls in school = 40%
percentage of boys in school = 100 – 40 = 60%
Number of boys in school = 60% of 2000 = 
× 2000
= 60 × 20 = 1200
Question 102.
Chalk contains 10% calcium, 3% carbon and 12% oxygen. Find the amount of carbon and calcium (in grams) in 
kg of chalk.
Answer:
Given, percentage of calcium in chalk = 10%
Percentage of carbon in chalk = 3%
Percentage of oxygen in chalk = 12%
∴ weight of chalk = kg = 
kg
= 2.5 × 1000 = 2500gm
⇒ Amount of carbon in chalk = 3% of 2500 = 
× 2500
= 75
⇒ Amount of Calcium in chalk = 10% of 2500 = × 2500
= 250
∴ amount of carbon and calcium respectively is 75 and 250
Question 103.
800 kg of mortar consists of 55% sand, 33% cement and rest lime. What is the mass of lime in mortar?
Answer:
Percentage of sand in motar = 55%
Percentage of cement in motar = 33%
Percentage of lime in motar = 100-55-33
= 100-88 = 12%
∴ Weight of motar = 800kg
∴ Mass of lime in mortar = 12% of 800kg
= × 800
= 96kg
Question 104.
In a furniture shop, 24 tables were bought at the rate of Rs 450 per table. The shopkeeper sold 16 of them at the rate of Rs 600 per table and the remaining at the rate of 400 per table. Find her gain or loss percent.
Answer:
Given, CP per table = 450
Number of tables = 24
⇒ CP of 24 tables = 24 × 450 = 10800
⇒ 16 tables sold at the rate of 600
∴ Sp of 16 tables = 16 × 600 = 9600
And remaining tables = 24-16 = 8
⇒ 8 tables sold at the rate of 400
⇒ SP for 8 tables = 8 × 400 = 3200
⇒ Total SP = 9600 + 3200
= 12800
∴ Profit or gain = SP-CP
= 12800-10800
= 2000
⇒ Gain = G
= 
= 18.51%
Question 105.
Medha deposited 20% of her money in a bank. After spending 20% of the remainder, she has Rs 4800 left with her. How much did she originally have?
Answer:
⇒ Let medha has originally x
⇒ Money deposited in bank = 20% of x = × x = 
⇒ Remaining money = x- = 
⇒ Money spent = 20% of remaining money = 
= 
⇒ Money left = 
= 
But given, money = 4800
⇒ 
= 4800
⇒ x = 
= 7500
Question 106.
The cost of a flower vase got increased by 12%. If the current cost is Rs 896, what was its original cost?
Answer:
⇒ Let the original cost be x
⇒ Now, the cost of flower vase is increased by 12%
⇒ x + 12% of x = 896
⇒ x + 
= 896
⇒ 
= 896
⇒ x = 
X = 800
Question 107.
Radhika borrowed Rs 12000 from her friends. Out of which Rs 4000 were borrowed at 18% and the remaining at 15% rate of interest per annum. What is the total interest after 3 years?
Answer:
For first year interest, we have
⇒ p1 = 4000, R1 = 18% and T1 = 3year
⇒ I1 =
= 
= 2160
For second year
⇒ P2 = 12000-4000 = 8000, R2 = 15% and T2 = 3year
⇒ I2 = 
= 
= 3600
Hence, after 3 year total interest = I1 + I2 = 2160 + 3600
= 5760
Question 108.
A man travelled 60 km by car and 240 km by train. Find what per cent of total journey did he travel by car and what per cent by train?
Answer:
Given, distance covered by car = 60km and
Distance covered by train = 240km
⇒ Total journey = 60 + 240 = 300km
⇒ Let x% of total journey is travelled by car
⇒ x% of 300 = 60
⇒ 
= 60
⇒ x = 20%
⇒ Let y% of total journey is travelled by train
⇒ y% of 300 = 240
⇒ 
= 240
⇒ y = 80%
Hence, 20% distance travelled by car and 80% distance travelled by train.
Question 109.
By selling a chair for Rs 1440, a shopkeeper loses 10%. At what price did he buy it?
Answer:
Given, SP = 1440 and loss = 10%
⇒ We know that Loss% = 
100%
⇒ Loss% = × 100%
⇒ 10 = 
⇒ 
= CP – 1440
⇒ CP - CP = 1440
⇒ 
CP = 1440
⇒ CP = 
⇒ CP = 1600
Question 110.
Dhruvika invested money for a period from May 2006 to April 2008 at rate of 12% per annum. If interest received by her is Rs 1620, find the money invested.
Answer:
Given, I = 1620 and R = 12%
Time = from May 2006 to April 2008 = 2 year
∵ I =
⇒ P = 
= 
= 6750
Question 111.
A person wanted to sell a scooter at a loss of 25%. But at the last moment he changed his mind and sold the scooter at a loss of 20%. If the difference in the two SP’s is Rs 4000, then find the CP of the scooter.
Answer:
⇒ Let the cost price of the scooter be x
⇒ If he sells the scooter at a loss of 25% then
⇒ SP = x-25% of x
= x- X
= x
And if he seels the scooter at a loss of 20% then
⇒ SP = x-20% of x
= x- x
= x
⇒ The difference in the two SP is 4000
∴ x-x = 4000
⇒ 
= 4000
⇒ x = 
= 80000
Question 112.
The population of a village is 8000. Out of these, 80% are literate and of these literate people, 40% are women. Find the ratio of the number of literate women to the total population.
Answer:
Given, total population = 8000
⇒ Literate people = 80% of total population
= × 8000 = 6400
⇒ Literate women = 40% of literate people = 
× 6400
= 2560
⇒ Ratio of literate women of total population = 2560 : 8000
= 8 : 25
Question 113.
In an entertainment programme, 250 tickets of Rs 400 and 500 tickets of Rs 100 were sold. If the entertainment tax is 40% on ticket of Rs 400 and 20% on ticket of Rs 100, find how much entertainment tax was collected from the programme.
Answer:
Given, 250 tickets of Rs 400 were sold
∴ total amount received by selling these tickets = 250 × 400 = 100000
⇒ Amount received by selling 500 tickets of Rs 100 = 500 × 100 = 50000
⇒ given, 40% and 20% of entertainment tax is on rs 400 and 100 tickets
∴ total entertainment tax collected = 40% of total amount received by selling tickets of rs 400 + 20% of total amount received by selling tickets of rs 100
= 40% of 100000 + 20% of 50000
= × 100000 + × 50000
= 40000 + 10000
= 50000
Question 114.
Bhavya earns Rs 50,000 per month and spends 80% of it. Due to pay revision, her monthly income increases by 20% but due to price rise, she has to spend 20% more. Find her new savings.
Answer:
Given, Bhavya earns 50000 per month
And spends 80% of 50000 = × 50000 = 40000
And savings per month = 50000-40000 = 10000
⇒ Given increment in monthly income = 20% of 50000
= × 50000 = 10000
⇒ Bhavya’s new income = 50000 + 10000 = 60000
⇒ Increase in expenditure = 20% of 40000 = × 40000 = 80000
⇒ new expenditure = 40000 + 8000 = 48000
⇒ Bhavya’s new savings = 60000-48000 = 12000
Question 115.
In an examination, there are three papers each of 100 marks. A candidate obtained 53 marks in the first and 75 marks in the second paper. How many marks must the candidate obtain in the third paper to get an overall of 70 per cent marks?
Answer:
⇒ Let x be the marks of candidate in thirs paper
⇒ total marks secured in all three papers = 53 + 75 + x
⇒ Total marks of three papers = 100 + 100 + 100 = 300
⇒ Percentage of marks = 
× 100%
= 
× 100%
⇒ Overall 70% of marks obtained
⇒ × 100 = 70
⇒ 
= 70
⇒ 128 + x = 210
⇒ x = 210 – 128
⇒ x = 82
Hence, 82 marks must be secured to get overall of 70% marks
Question 116.
Health Application
A doctor reports blood pressure in millimetres of mercury (mm Hg) as a ratio of systolic blood pressure to diastolic blood pressure (such as 140 over 80). Systolic pressure is measured when the heart beats, and diastolic pressure is measured when it rests. Refer to the table of blood pressure ranges for adults.
Manohar is a healthy 37 years old man whose blood pressure is in the normal category.
A. Calculate an approximate ratio of systolic to diastolic blood pressures in the normal range.
B. If Manohar’s systolic blood pressure is 102 mm Hg, use the ratio from part (a) to predict his diastolic blood pressure.
C. Calculate ratio of average systolic to average diastolic blood pressure in the prehypertension category.
Answer:
A) Systolic blood pressure in the normal range = 120mm Hg
Diastolic blood pressure in the normal range = 80mm
Approximate ratio of systolic to diastolic blood pressure = 
= 
=
∴ ratio = 3:2
B) Manohar’s systolic blood pressure = 102mm Hg
Let diastolic blood pressure = x mm Hg
Approximate ratio of systolic to diastolic blood pressure =
⇒ 
= 
⇒ x = 
⇒ X = 68mm Hg
C) Average systolic blood pressure in prehypertension category = 
= 
mm Hg
Average diastolic blood pressure in prehypertension category = 
= 
mm Hg
Hence, ratio of average systolic to average diastolic blood pressure = 
= 
= 
= 
Ratio is 259:169
Question 117.
(a) Science Application: The king cobra can reach a length of 558 cm. This is only about 60 per cent of the length of the largest reticulated python. Find the length of the largest reticulated python.
(b) Physical Science Application: Unequal masses will not balance on a fulcrum if they are at equal distance from it; one side will go up and the other side will go down.
Unequal masses will balance when the following proportion is true:
Two children can be balanced on a seesaw when. The child on the left and child on the right are balanced. What is the mass of the child on the right?
(c) Life Science Application
A DNA model was built using the scale 2 cm : 0.0000001 mm. If the model of the DNA chain is 17 cm long, what is the length of the actual chain?
Answer:
a) ⇒ Length of the King cobra = 558cm
⇒ 60% of length of reticulated python = 558cm
⇒ × Length of retuiculated phython = 558cm
∴ Length of reticulated python = 558 × 
= 930cm
b) Given, 
= 
⇒ Mass1 = 24 kg, length1 = 3m and length2 = 2m
⇒ 
= 
⇒ Mass2 = 36kg
c) ⇒ Length of the chain be xmm
∴ 
= 
⇒ x = 
⇒ X = 0.00000085
Question 118.
Language Application
Given below are few Mathematical terms.
Find
A. The ratio of consonants to vowels in each of the terms.
B. The percentage of consonants in each of the terms.
Answer:
⇒ Ratio of consonants to vowels = 
a) In term “Hypotenuse” 6 consonants and 4 vowels are there
∴ 
=
= 3:2
⇒ In term “Congruence” 6 consonants and 4 vowels are there
∴ =
= 3:2
⇒ In term “Perpendicular” 8 consonants and 5 vowels are there
∴ 
= 8:5
⇒ In term “Transversal” 8 consonants and 3 vowels are there
∴ 
= 8:3
⇒ In term “Correspondence” 9 consonants and 5 vowels are there
∴ 
= 9:5
b) Percentage of consonants = 
× 100%
Total number of letters = Number of consonants + number of vowels
⇒ In term “Hypotenuse” total number of letters = 6 + 4 = 10
= × 100% = 60%
⇒ In term “Congruence” total number of letters = 6 + 4 = 10
= × 100% = 60%
⇒ In term “Perpendicular” total number of letters = 8 + 5 = 13
= 
× 100% = 61.53%
⇒ In term “Transversal” total number of letters = 8 + 3 = 11
= 
× 100% = 72.72%
⇒ In term “Correspondence” total number of letters = 9 + 5 = 14
= 
× 100% = 64.28%
Question 119.
What’s the Error? An analysis showed that 0.06 per cent of the T-shirts made by one company were defective. A student says this is 6 out of every 100. What is the student’s error?
Answer:
⇒ Defective T-shirts mad by one company = 0.06% = 
⇒ as per student defective T-shirt = 6 out of every 100 =
Hence, defective T-shirts are 6 out of every 1000
Question 120.
What’s the Error? A student said that the ratios 
and 
were proportional. What error did the student make?
Answer:
Two ratios a:b and C:d are said to be proportional, if 
= 
But given, and 
⇒ 3 × 16 not equal to 4× 9
Question 121.
What’s the Error? A clothing store charges Rs 1024 for 4 T-shirts. A student says that the unit price is Rs 25.6 per T-shirt. What is the error? What is the correct unit price?
Answer:
⇒ Cost of 4 T-shirts = 1024
⇒ Cost of 1 T-shirt = 
= 256
∴ the correct unit price = 256
Question 122.
A tea merchant blends two varieties of tea in the ratio of 5 : 4. The cost of first variety is Rs 200 per kg and that of second variety is Rs 300 per kg. If he sells the blended tea at the rate of Rs 275 per kg, find out the percentage of her profit or loss.
Answer:
Given, ratio of blended two varieties of tea = 5:4
And cost of green tea = 200 per kg
And cost of lemon tea = 300 per kg
SP of blended tea = 275 per kg
⇒ Let green tea be 5x kg and lemon be 4x kg
⇒ Cost of lemon tea = 4x × 300 = 1200x
⇒ Cost of green tea = 5x × 200 = 1000x
⇒ Total CP = 1000x + 1200x = 2200x
⇒ Total quantitiy = 4X + 5X = 9X
∴ SP of blended tea = 275 × 9x = 2475x
∵ CP <SP
So, there is profit on blended tea
⇒ Profit = SP-CP
= 2475x – 2200x = 275x
⇒ Profit% = × 100%
= 
× 100%
= 
= 12.5%
Question 123.
A piece of cloth 5 m long shrinks 10 per cent on washing. How long will the cloth be after washing?
Answer:
⇒ Length of shrink cloth = 10% of 5m = × 5 = 
∴ Length of cloth after wash = 5-
= 
= 4.5m
Question 124.
Nancy obtained 426 marks out of 600 and the marks obtained by Rohit are 560 out of 800. Whose performance is better?
Answer:
Given, Nancy got marks = 426 out of 600
⇒ Percentage marks = 
× 100% = 71%
⇒ Rohit got marks = 560 out of 800
⇒ Percentage marks = 
× 100% = 70%
Question 125.
A memorial trust donates Rs 5,00,000 to a school, the interest on which is to be used for awarding 3 scholarships to students obtaining first three positions in the school examination every year. If the donation earns an interest of 12 per cent per annum and the values of the second and third scholarships are Rs 20,000 and Rs 15,000 respectively, find out the value of the first scholarship.
Answer:
Given, Donation amount = 500000
And Rate of interest for each year = 12% per annum
Time period = 1 year
⇒ Interest received after 1 year = 
= 5000 × 12
⇒ Scholarship amount for second position = 20000
⇒ Scholarship amount for third position = 15000
⇒ Remaining amount for first position student = 60000 –(20000 + 15000)
= 25000
Question 126.
Ambika got 99 per cent marks in Mathematics, 76 per cent marks in Hindi, 61 per cent in English, 84 per cent in Science, and 95% in Social Science. If each subject carries 100 marks, then find the percentage of marks obtained by Ambika in the aggregate of all the subjects.
Answer:
Given, each subject carries 100 marks
⇒ Ambika got marks as follows:
Mathematics = 99, Hindi = 76, English = 61, Science = 84 and Social science = 95
∴ aggregate marks = 
× 100%
= 
× 100% = 
= 83%
Question 127.
What sum of money lent out at 16 per cent per annum simple interest would produceRs 9600 as interest in 2 years?
Answer:
Given, I = 9600, T = 2year and R = 16%
⇒ we know that I =
∴ P =
= 
= 30000
Question 128.
Harish bought a gas-chullah for Rs 900 and later sold it to Archana at a profit of 5 per cent. Archana used it for a period of two years and later sold it to Babita at a loss of 20 per cent. For how much did Babita get it?
Answer:
Given, Chullah was bought for 900 and sold at a 5% profit
⇒ CP of Chullah for ARchana = 900 + 5% of 900
= 900 + 
× 900
= 900 + 45 = 945
⇒ ARchana sold chullah for Babita at a loss of 20%
∴ CP of chullah for Babita = 945 – 20% of 945
= 945 - × 945
= 945 – 189
= 756
Question 129.
Match each of the entries in Column I with the appropriate entries in Column II:
Column I
i. 3:5
ii. 2.5
iii. 100%
iv. 
v. 
vi. 12.5%
vii. SP when CP = Rs 50 and loss = 6%
viii. SP when CP = Rs 50 and profit = Rs 4
ix. Profit % when CP = Rs 40 and SP = Rs 50
x. Profit when CP = Rs 50 and SP = Rs 60
xi. Interest when principal = Rs 800,
Rate of interest = 10% per annum and period = 2 years
xii. Amount when principal = Rs 150, Rate of interest = 6% per annum and period = 1 year
Column II
A. Rs 54
B. Rs 47
C. Rs 53
D. Rs 160
E. 60%
F. 25%
G. 
H. 250%
I. Rs 159
J. 
K. 20%
L. 0.125
M. 3 : 2
N. Rs 164
O. 3 : 3
Answer:
i) Mathces to E
Given, ratio = 3:5
In Percentage, × 100% = 60%
ii) Matches H
Given, 2.5
In Percentage, 2.5 × 100% = 250%
iii) Matches O
Given, 100%
⇒ Ratio = 100%:1
= : 1
⇒ Ratio = 1:1
= 1× 3:1×3
= 3:3
iv) Matches J
Given, 
In Percentage, × 100% = %
v) Matches G
Given, 
= 
For Fraction, 
× 
= 
vi) Matches L
Given, 12.5%
For fraction, 
= 
For decimal, = 0.125
vii) Matches B
Given, CP = 50, Loss% = 6%
⇒ Loss% = × 100%
= 
× 100%
⇒ 6 = 
× 100
SP = 47
viii) Matches A
Given, CP = 50, Profit = 4
⇒ Profit = SP-CP
⇒ SP = Profit + Cp
= 4 + 50 = 54
ix) Matches F
Given, Cp = 40, SP = 50
⇒ Profit = SP-CP
= 50-40 = 10
Profit% = × 100% = 
× 100%
Profit% = 25%
x) Matches K
Given, CP = 50, SP = 60
⇒ Profit = SP-CP
= 60-50 = 10
Profit% = × 100% = 
× 100%
Profit% = 20%
xi) Matches D
Given, P = 800, R = 10%, T = 2year
⇒ I = 
⇒ I = 160
xii) Matches l
Given, P = 150, R = 6%, T = 1year
Need to find out A
⇒ I = 
= 9
⇒ A = P + I
= 159
Question 130.
In a debate competition, the judges decide that 20 per cent of the total marks would be given for accent and presentation. 60 per cent of the rest are reserved for the subject matter and the rest are for rebuttal. If this means 8 marks for rebuttal, then find the total marks.
Answer:
⇒ Let x be the total marks
⇒ Marks given for accent and presentation = 20% of x = × x = 
⇒ Remaining marks = x – 
= 
⇒ Marks reserved for subject matter = 60% of rest marks = × = 
⇒ Now, remaining marks = – 
= 
∴ = 8
⇒ x = 25
Question 131.
Divide Rs 10000 in two parts so that the simple interest on the first part for 4 years at 12 per cent per annum may be equal to the simple interest on the second part for 4.5 years at 16 per cent per annum.
Answer:
Given, money = 10000
Money should be divided into two parts, SI on first part for 4yr at 12% and SI on second part for 4.5yr at 16%
Let first part = 7X
Secon part = (10000-x)
⇒ SI1 = = 
⇒ SI2 = = 
⇒ 
=
⇒ 
= (10000 –x)
⇒ 
= (10000 –x)
⇒ x = 10000-x
⇒ 
= 10000
⇒ x = 6000
⇒ First part = 6000
⇒ Second part = 10000-x = 10000-6000 = 4000
Question 132.
Rs 9000 becomes Rs 18000 at simple interest in 8 years. Find the rate per cent per annum.
Answer:
Given, P = 9000, A = 18000 and T = 8year
⇒ We know that A = P + I
⇒ I = A-P
= 18000-9000
= 9000
⇒ we know that, I =
⇒ R = 
= 
= 12.5%
Question 133.
In how many years will the simple interest on a certain sum be 4.05 times the principal at 13.5 per cent per annum?
Answer:
⇒ Let Principal = P, R = 13.5%, I = 4.05 times principal = 4.05 × P
Need to find T
⇒ we know that, I =
⇒ 4.05 × P = 
⇒ T = 
= 
= 30year
Question 134.
The simple interest on a certain sum for 8 years at 12 per cent per annum is Rs 3120 more than the simple interest on the same sum for 5 years at 14 per cent per annum. Find the sum.
Answer:
⇒ Let the sum be x
Given, P1 = x, R1 = 12% and T1 = 8 year and
P2 = x, R2 = 14% and T2 = 5 year
⇒ The difference between I1 and I2 is 3120
⇒ I1-I2 = 3120
⇒ – = 3120
⇒ 
- 
= 3120
⇒ 96x- 70x = 3120 × 100
⇒ 26x = 312000
⇒ x = 12000
Question 135.
The simple interest on a certain sum for 2.5 years at 12 per cent per annum is Rs 300 less than the simple interest on the same sum for 4.5 years at 8 per cent per annum. Find the sum.
Answer:
⇒ Let the sum be x
Given, P1 = x, R1 = 12% and T1 = 2.5year = year and
P2 = x, R2 = 8% and T2 = 4.5 year = year
⇒ The difference between I1 and I2 is 300
⇒ I2-I1 = 300
⇒ - = 300
⇒ 
- 
= 300
⇒ 72x- 60x = 300 × 200
⇒ 12x = 60000
⇒ x = 5000
Question 136.
Designing a Healthy Diet
When you design your healthy diet, you want to make sure that you meet the dietary requirements to help you grow into a healthy adult. As you plan your menu, follow the following guidelines
1. Calculate your ideal weight as per your height from the table given at the end of this question.
2. An active child should eat around 55.11 calories for each kilogram desired weight.
3. 55 per cent of calories should come from carbohydrates. There are 4 calories in each gram of carbohydrates.
4. 15 per cent of your calories should come from proteins. There are 4 calories in each gram of proteins.
5. 30 per cent of your calories may come from fats. There are 9 calories in each gram of fat.
Following is an example to design your own healthy diet.
Example
1. Ideal weight = 40 kg.
2. The number of calories needed = 40 × 55.11 = 2204.4
3. Calories that should come from carbohydrates
= 2204.4 × 0.55 = 1212.42 calories.
Therefore, required quantity of carbohydrates
4. Calories that should come from proteins
= 2204.4 × 0.15 = 330.66 calories.
Therefore, required quantity of protein
5. Calories that may come from fat = 2204.4 × 0.3 = 661.3 calories.
Therefore, required quantity of fat
Questions
1. Your ideal desired weight is _________ kg.
2. The quantity of calories you need to eat is _______.
3. The quantity of protein needed is _______g.
4. The quantity of fat required is _________ g.
5. The quantity of carbohydrates required is __________ g.
Answer:
1) ⇒ Let the height be 5ft
⇒ According to the table idle weight = 48kg
2) The quantity of calories needed = 48 × 55.11 = 2645.28 calories
3) Calorie that should come from proteins = 2645.28 × 0.15 = 396.79 calories
∴ required quantitiy of protein = 
= 99.19g
4) Calories that may come from fats = 2645.28 × 0.3 = 793.5 calories
∴ required quantity of fats = 
= 88.17g
5) Calorie that should come from carbohydrates = 2645.28 × 0.55 = 1454.90 calories
∴ required quantity of carbohydrates = 
= 363.72 = 360
Question 137.
150 students are studying English, Maths or both. 62 per cent of students study English and 68 per cent are studying Maths. How many students are studying both?
Answer:
Given, total students = 150
⇒ Students who study in English = 62% of 150 = 
× 150 = 93
⇒ Students who study Maths = 68% of 150 = 
× 150 = 102
⇒ Total students = 93 + 102 = 195
∴ students who study both English and maths = 195-150 = 142
Question 138.
Earth Science: The table lists the world’s 10 largest deserts.
A. What are the mean, median and mode of the areas listed?
B. How many times the size of the Gobi Desert is the Namib Desert?
C. What percentage of the deserts listed are in Asia?
D. What percentage of the total area of the deserts listed is in Asia?
Answer:
A) Mean = 
⇒ Total area of all deserts = 8800000 + 1300000 + 1250000 + 850000 + 580000 + 370000 + 320000 + 310000 + 310000 + 260000 = 14350000
= [
]
= 1435000 km2
⇒ Median = [
]
= [
]
= 
= 
= 475000 km2
⇒ Mode = Most frequent observation = 310000 km2
B) Let the size of Gobi desert is x times the Namib desert
∴ Gobi desert = x × Namib desert
⇒ 1300000 = x × 310000
⇒ x = 
= 4.19
C) ⇒ Total number of deserts = 10
⇒ Number of deserts in Asia = 5
∴ percentage of deserts in Asia = 
× 100% = 50%
D) ⇒ Total area of all deserts = 14350000 km2
⇒ Total area of Asia’s deserts = 1300000 + 850000
= 3040000 km2
∴ percentage of the total area of the deserts listed in Asia = 
= 
× 100%
Question 139.
Geography Application: Earth’s total land area is about 148428950 km2. The land area of Asia is about 30 per cent of this total. What is the approximate land area of Asia to the nearest square km?
Answer:
Given, total land area of Earth = 148428950km2
⇒ Land area of Asia = 30% of land area of earth
= 
× 148428950
= 44528685km2
Question 140.
The pieces of Tangrams have been rearranged to make the given shape.
By observing the given shape, answer the following questions:
• What percentage of total has been coloured?
(i) Red (R) = _________
(ii) Blue (B) = ________
(iii) Green (G) = _______
• Check that the sum of all the percentages calculated above should be 100.
• If we rearrange the same pieces to form some other shape, will the percentage of colours change?
Answer:
1) Total coloured shape = 
+ + + + + + = 1
i) Red coloured shape = + + =
Percentage of Red coloured = 
× 100%
= 
= 37.5%
ii) Blue coloured shape = + =
Percentage of blue coloured shape = 
× 100%
= × 100%
iii) Green coloured shape = +
=
Percentage of green coloured shape = 
× 100%
= × 100%
2) Sum of all percentages calculated = Percentage of red coloured + percentage of blue coloured + percentage of green coloured
= 37.5 + 50 + 12.5
= 100%
3) If we rearrange the same pieces to form some other shape, the percentage of colours will not change, because we just rearrange the parts and not changing the percentage of colours.