Percentage
Class 8th Mathematics RD Sharma Solution
- Write each of the following as percentage. (i) 7/25 (ii) 14/625 (iii) 5/8 (iv)…
- Convert the following percentages to fractions and ratios. (i) 25% (ii) 2.5%…
- Express the following as decimal fractions. (i) 27% (ii) 6.3% (iii) 32%…
- Find: (i) 22% of 120 (ii) 25% of Rs 1000 (iii) 25% of 10 kg (iv) 16.5% of 5000…
- Find the number a, if (i) 8.4% of a is 42 (ii) 0.5 of a is 3 (iii) 1/2 of a is…
- x is 5% of y, y is 24% of z. If x = 480, find the values of y and z.…
- A coolie deposits Rs 150 per month in his post office Savings Bank account. If…
- Asha got 86.875% marks in the annual examination. If she got 695 marks, find…
- Deepti went to school for 216 days in a full year. If her attendance is 90%,…
- A garden has 2000 trees. 12% of these are mango trees 18% lemon and the rest…
- Balanced diet should contain 12% of proteins, 25% of fats and 63% of…
- A cricketer scored a total of 62 runs in 96 balls. He hit 3 sixes, 8 fours, 2…
- A cricketer hit 120 runs in 150 balls during a test match. 20% of the runs…
- Radha earns 22% of her investment. If she earns Rs 187, Then how much did she…
- Rohit deposits 12% of his income in a bank. He deposited Rs 1440 in the bank…
- Gunpowder contains 75% nitre and 10% sulphur. Find the amount of the gunpowder…
- An alloy of tin and copper consists of 15 parts of tin and 105 parts of…
- An alloy contains 32% copper, 40% nickel and rest zinc. Find the mass of the…
- A motorist travelled 122 kilometres before his first stop. If he had 10%of his…
- A certain school has 300 students, 142 of whom are boys. It has 30 teachers,…
- Amans income is 20% less than that of Anil. How much percent is Anils income…
- The value of a machine depreciates every year by 5%. If the present value of…
- The population of a town increases by 10% annually. If the present population…
- The population of a town increases by 10% annually. If the present population…
- Ankit was given an increment of 10% on his salary. His new salary is Rs3575.…
- In the new budget, the price of petrol rose by 10%. By how much percent must…
- Mohans income is Rs 15500 per month. He saves 11%. of his income. If his…
- Shikhas income is 60% more than that of Shalu. What percent is Shalus income…
- Rs 3500 is to be shared among three people so that the first person gets 50%of…
- After a 20% hike, the cost of Chinese Vase is Rs 2000. What was the original…
Exercise 12.1
Question 1.Write each of the following as percentage.
(i) 7/25
(ii) 14/625
(iii) 5/8
(iv) 0.8
(v) 5/8
(vi) 0.8
(vii) 11 : 80
(viii) 111 : 125
(ix) 13 : 75
(x) 15 : 16
(xi) 0.18
(xii) 7/125
Answer:
(i) 7/25
We know that while changing in percentage we have to multiplied by 100, so,
= 
(ii) 14/625
We know that while changing in percentage we have to multiplied by 100, so,
= 
(iii) 5/8
We know that while changing in percentage we have to multiplied by 100, so,
= 
(iv) 0.8
We know that while changing in percentage we have to multiplied by 100, so,
= 
(v) 5/8
We know that while changing in percentage we have to multiplied by 100, so,
=
(vi) 0.8
We know that while changing in percentage we have to multiplied by 100, so,
=
(vii) 11 : 80
We know that while changing in percentage we have to multiplied by 100, so,
= 
(viii) 111 : 125
We know that while changing in percentage we have to multiplied by 100, so,
= 
(ix) 13 : 75
We know that while changing in percentage we have to multiplied by 100, so,
= 
(x) 15 : 16
We know that while changing in percentage we have to multiplied by 100, so,
= 
(xi) 0.18
We know that while changing in percentage we have to multiplied by 100, so,
= 
(xii) 7/125
We know that while changing in percentage we have to multiplied by 100, so,
= 
Question 2.
Convert the following percentages to fractions and ratios.
(i) 25%
(ii) 2.5%
(iii) 0.25%
(iv) 0.3%
(v) 125%
Answer:
(i) 25%
The required fraction is,
= 
(ii) 2.5%
The required fraction is,
= 
(iii) 0.25%
The required fraction is,
= 
(iv) 0.3%
The required fraction is,
= 
(v) 125%
The required fraction is,
= 
Question 3.
Express the following as decimal fractions.
(i) 27%
(ii) 6.3%
(iii) 32%
(iv) 7.5%
(v) 1/8%
Answer:
(i) 27%
The required decimal fraction is,
= 
(ii) 6.3%
The required decimal fraction is,
= 
(iii) 32%
The required decimal fraction is,
= 
(iv) 7.5%
The required decimal fraction is,
= 
.
(v) 
The required decimal fraction is,
= 
Exercise 12.2
Question 1.Find:
(i) 22% of 120
(ii) 25% of Rs 1000
(iii) 25% of 10 kg
(iv) 16.5% of 5000 metre
(v) 135% of 80 cm
(vi) 2.5% of 10000 ml
Answer:
(i) 22% of 120
(ii) 25% of Rs 1000
(iii) 25% of 10 kg
(iv) 16.5% of 5000 metre
(v) 135% of 80 cm
(vi) 2.5% of 10000 ml
Question 2.
Find the number a, if
(i) 8.4% of a is 42
(ii) 0.5 of a is 3
(iii) 
of a is 50
(iv) 100% of a is 100
Answer:
(i) 8.4% of a is 42
= a = 
(ii) 0.5 of a is 3
= 
(iii) of a is 50
= a = 50×2 = 100
(iv) 100% of a is 100
= 
Question 3.
x is 5% of y, y is 24% of z. If x = 480, find the values of y and z.
Answer:
Given x = 480
Ans, x is 5% of y.
So, we write it as:
solving for y, we get,
or y = 9600
Now, It is also given that: y is 24% of z
Therefore, we can write it as:
or 9600 = 24z/ 100
Solving it for z we get, z = 960000/24
z = 40000
Question 4.
A coolie deposits Rs 150 per month in his post office Savings Bank account. If this is 15% of his monthly income, find his monthly income.
Answer:
Let his monthly income be = Rs. x
=
=
Question 5.
Asha got 86.875% marks in the annual examination. If she got 695 marks, find the total number of marks of the examination.
Answer:
Marks got by asha = 695
Percentage of marks got by asha = 86.875%
Let total marks are = x
Hence,
= 
= 
∴ Total number of marks = 800
Question 6.
Deepti went to school for 216 days in a full year. If her attendance is 90%, find the number of days on which the school was opened.
Answer:
Number of days she went to school = 216 days
Attendence percentage = 90%
Let number of days for which school was opened = x
Hence,
=
= 
Question 7.
A garden has 2000 trees. 12% of these are mango trees 18% lemon and the rest are orange trees. Find the number of orange trees.
Answer:
Given,
Total number of trees = 2000
Number of mango trees = 
Number of lemon trees = 
Hence,
Number of orange trees = 2000 – (no.of mango trees+ no. of lemon trees)
= 2000 – (240+360)
= 2000 – 600 = 1400 trees
Question 8.
Balanced diet should contain 12% of proteins, 25% of fats and 63% of carbohydrates. If a child needs 2600 calories in this food daily, find in calories the amount of each of these in his daily food intake.
Answer:
Amount of calorie daily needed = 2600 calorie
Amount of protein needed = 
Amount of fats needed = 
Amount of carbohydrate needed = 
Question 9.
A cricketer scored a total of 62 runs in 96 balls. He hit 3 sixes, 8 fours, 2 twos and 8 singles. What percentage of the total runs came in
(i) Sixes
(ii) 4’s
(iii) 2’s
(iv) singles
Answer:
Total runs scored by cricketer = 62
(i) Run scored in 3 sixes = 3×6 = 18
Percentage of runs scored in sixes = 
(ii) Run scored in 8 fours = 8×4 = 32
Percentage of runs scored in fours = 
(iii) Run scored in 2 two’s = 2×2 = 4
Percentage of runs scored in two’s = 
(iv) Run scored in singles = 8
Percentage of runs scored in singles = 
Question 10.
A cricketer hit 120 runs in 150 balls during a test match. 20% of the runs came in 6’s, 30% in 4’s, 25% in 2’s and the rest in 1’s. How many runs did he score in
(i) 6’s (ii) 4’s
(iii) 2’s (iv) singles
What % of his shots were scoring ones?
Answer:
Total number of runs scored by cricketer = 120
i) Number of runs he scored in 6’s = 
ii) Number of runs he scored in 4’s =
iii) Number of runs he scored in 2’s = 
iv) Number of runs he scored in singles = 120 – (24+36+30)
= 120 – 90 = 30
Percentage of shots scoring ones:
Question 11.
Radha earns 22% of her investment. If she earns Rs 187, Then how much did she invest?
Answer:
Percentage earn of Radha = 22% of investment
Let total investment = Rs. X
So,
= 
= 
∴ Total investment made by Radha = Rs.350
Question 12.
Rohit deposits 12% of his income in a bank. He deposited Rs 1440 in the bank during 1997. What was his total income for the year 1997?
Answer:
Percentage deposit by Rohit in bank = 12% of total income
Money actually deposited by him = Rs. 1440
Let total income of Rohit = Rs. X
So,
∴ Total income of Rohit = Rs.12000
Question 13.
Gunpowder contains 75% nitre and 10% sulphur. Find the amount of the gunpowder which carries 9 kg nitre. What amount of gunpowder would contain 2.3 kg sulphur?
Answer:
Amount of nitre in gunpowder = 9 kg
Percentage of nitre in gunpowder = 75%
Let amount of gunpowder = x kg
So,
= 
= 
Amount of sulphur in gunpowder = 2.3 kg
Percentage of sulphur in gunpowder = 10%
Let amount of gunpoder = x kg
So,
=
=
Question 14.
An alloy of tin and copper consists of 15 parts of tin and 105 parts of copper. Find the percentage of copper in the alloy?
Answer:
In an alloy,
Amount of tin = 15 part
Amount of copper = 105 part
Total weight of alloy = 15+105 = 120
Hence,
Percentage of copper in alloy = 
Question 15.
An alloy contains 32% copper, 40% nickel and rest zinc. Find the mass of the zinc in 1 kg of the alloy.
Answer:
Mass of alloy = 1kg = 1000 gm
Mass of copper in alloy = 
Mass of nickel in alloy = 
So, amount of zinc in alloy = 1000 - (320 + 400) = 1000 – 720 = 280 gm
Question 16.
A motorist travelled 122 kilometres before his first stop. If he had 10%of his journey to complete at this point, how long was the total ride?
Answer:
Total distance travelled before first stop = 122 km
Distance completed at first stop = 10 %
Let total distance to be travelled = x km
So,
= 
∴ Total distance = 1220 km
Question 17.
A certain school has 300 students, 142 of whom are boys. It has 30 teachers, 12 of whom are men. What percent of the total number of students and teaachers in the school is female?
Answer:
Number of students in school = 300
Number of boys = 142
∴ Number of girls = 300 – 142 = 158
Number of teachers in school = 30
No. of male teachers = 12
∴ No. of female teachers = 30 – 12 = 18
Total no. of students and teachers = 300+30 = 330
Total numbers of females = 158+18 = 176
Percentage of females in school = 
Question 18.
Aman’s income is 20% less than that of Anil. How much percent is Anil’s income more than Aman’s income?
Answer:
Let Anil’s income = Rs. X
Aman’s income = 
Difference between Anil’s and Aman’s income = 
Hence,
Percentage in which Anil’s income is more than Aman’s income =
Question 19.
The value of a machine depreciates every year by 5%. If the present value of the machine be Rs 100000, what will be its value after 2 years?
Answer:
Present value of machine = Rs.100000
Depreciation in price every year = 5%
Hence,
= Rs.90250
Question 20.
The population of a town increases by 10% annually. If the present population is 600000, what will be its population after 2 years?
Answer:
Present population of town = 60000
Percentage increase in population annually = 10%
Hence ,
Population of town after 2 years = 
(time in years)
= 72600
Question 21.
The population of a town increases by 10% annually. If the present population is 22000, find its population a year ago.
Answer:
Present population of town = 22000
Increase in population annually = 10%
Hence,
Population of town one year ago = 
(time in years)
= 
Question 22.
Ankit was given an increment of 10% on his salary. His new salary is Rs3575. What was his salary before increment?
Answer:
New salary of Ankit = Rs.3575
Percentage increase in salary = 10%
Let original salary of Ankit is = Rs. X
Hence,
Salary of Ankit before increment = 
= 
∴ Original salary of Ankit = Rs. 3250
Question 23.
In the new budget, the price of petrol rose by 10%. By how much percent must one reduce the consumption so that the expenditure does not increase?
Answer:
Percentage increase in price of petrol = 10%
Hence,
Reduction in consumption while having same expenditure =
Question 24.
Mohan’s income is Rs 15500 per month. He saves 11%. of his income. If his income increases by 10%, then he reduces his saving by 1%, how much does he save now?
Answer:
Monthly income of mohan = Rs.15500
Saving of mohan = 11% of 15500 = 
Increase in monthly income = 10%
New monthly income = 
New saving percentage = 11 – 1 = 10%
Hence,
New amount of saving = 
∴ saving remains same.
Question 25.
Shikha’s income is 60% more than that of Shalu. What percent is Shalu’s income less than Shikha’s?
Answer:
Let shalu’s income = Rs. X
Hence, shikha’s income = 
Difference between shikha’s and shalu’s income = 
Hence,
Percentage in which shalu’s income is less than shikha’s income =
Question 26.
Rs 3500 is to be shared among three people so that the first person gets 50%of the second, who in turn gets 50% of the third. How much will each of them get?
Answer:
Total money to be shared = Rs. 3500
Let third person get = Rs. X
So, second person gets = 
First person gets = 50% of 
We know that,
= 
= 
= 
∴ third person get = Rs. 2000
∴ second person get = 
∴ first person get = 
Question 27.
After a 20% hike, the cost of Chinese Vase is Rs 2000. What was the original price of the object?
Answer:
The Cost of chinese vase after hike = Rs. 2000
Percentage hike = 20%
Let original price of chinese vase = Rs. X
Hence,
= 
= 
= 
∴ original price of chinese vase = Rs. 1666.67