Simple Interest
Class 10th Mathematics West Bengal Board Solution
- Two friends together took a loan amount ₹15,000 to run a business from a bank at the…
- Let us determine the interest of ₹2000 at the rate if simple interest of 6% per annum…
- Let us determine the amount (Principal along with interest)of ₹960 at the rate of…
- Utplalbabu took a loan ₹3200 for 2 yrs. From a Cooperative bank for the cultivation of…
- Sovadebi deposited some amount of money in a bank at the rate of simple interest of…
- Goutam took a loan of some money from a Cooperative bank for opening a poultry farm…
- Let us write by calculating, the number of yrs for which an amount becomes twice of its…
- Mannan Miyan observed, after 6 years of taking a loan of some money, that the interest…
- An agricultural Co-operative society gives agricultural loan to its members at the rate…
- If the interest of ₹292 in 1 day be 1 paise, then let us write by calculating, the…
- Let us write, by calculating the number of yrs. for which the interest of ₹600 at the…
- If I get ₹1200 return as amount (principal along with interest) by depositing ₹800in…
- At the same rate of simple interest in percent per annum, if a principal becomes the…
- Amal Roy deposits ₹2000 in the bank and Poshupoti Ghosh deposits ₹2000 in the post…
- A weaver Cooperative society takes a loan of ₹15,000 at the time of buying a power…
- Aslamchacha got ₹1,00,00 when he retired from his service. He deposited some of that…
- Rekhadidi deposited ₹10,000 of her savings in two separate banks at the same time. The…
- A bank gives 5% simple interest per annum. In the bank, Dipubabu deposits₹ 15,000 at…
- Rahamatchacha takes a loan amount of ₹2,40,000 from a bank for constructing a building…
- Rothinbabu deposits the money for each of his two daughters in such a way that when…
- Q21A1 If the interest of ₹p at the rate of simple interest of r% per annum in t years is…
- Q21A2 A principal becomes twice of its amount in 20 yrs at a certain rate of…
- Q21A3 If a principal becomes twice of its amount in 10 yrs, the rate of simple interest…
- Q21A4 If the total interest becomes ₹ x for any principal having the rate of simple…
- Q21A5 The total interest of a principal in n yrs. at the rate of simple interest of r% per…
- Let us write, whether the following statements are true or false: (i) A man takes a…
- Let us fill in the blanks: (i) A man who gives a loan is called___________. (ii) The…
- Let us write the number of yrs. for which a principal becomes twice of its amount…
- The rate of simple interest per annum reduces 4% to 3 3/4 % and for this, Amalbabu’s…
- What is the rate of simple interest per annum, when the interest of some money in 4…
- What is the rate of simple interest per annum, when the interest of some money in…
- Let us determine the money for which monthly interest is ₹1 having the rate of simple…
Let Us Work Out 2
Question 1.Two friends together took a loan amount ₹15,000 to run a business from a bank at the rate of simple interest of 12% per annum. Let us write, by calculating, the interest they have to pay after 4 yrs.
Answer:
In mathematical language, the problem is
In that bank, the rate of simple interest is 12%.
So, the interest of Rs. 100 in 1 yr is Rs. 12
The interest of Rs. 1 in 1 yr is Rs. 
⇒ The interest of Rs. 15,000 in 1 yr is 
= Rs. 1,800
⇒ The interest of Rs. 15,000 in 4 yr is 
= Rs. 7,200
The total interest paid by them = Rs. 7,200
Question 2.
Let us determine the interest of ₹2000 at the rate if simple interest of 6% per annum from 1st January to 26th May, 2005.
Answer:
Time = January 31 days + February 28 days + March 31 days + April 30 days + May 25 days
= 145 Days
In mathematical language the problem is
So, the interest of Rs. 100 in 1 yr is Rs. 6
⇒ The interest of Rs. 1 in 1 yr is Rs. 
⇒ The interest of Rs. 2000 in 1 yr is
= Rs. 120
⇒ The interest of Rs. 2,000 in 
yr is
= Rs. 267.7
The total interest paid by them = Rs. 267.7
Question 3.
Let us determine the amount (Principal along with interest)of ₹960 at the rate of simple interest of 
% annum for 1 yr. 3months.
Answer:
Time = 1 yr + 3 months
3months 
yr
In mathematical language, the problem is
So, the interest of Rs. 100 in 1 yr is Rs. 
⇒ The interest of Rs. 1 in 1 yr is Rs. 
⇒ The interest of Rs. 960 in 1 yr is Rs.
= Rs. 80
⇒ The interest rate of Rs. 960 in 
yr is
= Rs. 100
Amount (Principal along with interest)
= Interest + Principal
= 100 + 960 = Rs. 1060
Question 4.
Utplalbabu took a loan ₹3200 for 2 yrs. From a Cooperative bank for the cultivation of his land at the rate of simple interest of 6% per annum. Let us write by calculating, the amount he has to repay after 2yrs.
Answer:
As we know,
Here, p = Rs. 3200, r = 6 , t = 2 and I = ?
⇒ 
= Rs. 384
Amount (Principal along with interest)
= Interest + Principal
= 384 + 3200 = Rs. 3584
Hence, Rs. 3200 he has to pay after 2 yrs.
Question 5.
Sovadebi deposited some amount of money in a bank at the rate of simple interest of 5.25% per annum. After 2yrs. She has got ₹840 as interest. Let us write by calculating, the money she has deposited in the bank.
Answer:
As we know,
Here, P = ?, r = 5.25 t = 2 and I = Rs. 840
= Rs. 8000
Hence, she has deposited Rs. 8000 in the bank.
Question 6.
Goutam took a loan of some money from a Cooperative bank for opening a poultry farm atthe rate of simple interest of 12% per annum. Every month he has to repay ₹378 as interest. Let us determine the loan amount taken by him.
Answer:
Time = 1 month = 
yr
As we know,
Here, P = ?, r = 12, t = yr and I = Rs. 378
= Rs. 37800
Hence, loan amount taken by him Rs. 37800
Question 7.
Let us write by calculating, the number of yrs for which an amount becomes twice of its principal having the rate of simple interest of 6% per annum.
Answer:
Interest = Amount – Principal
Let, Principal = p, Amount = 2p
⇒ Interest = 2p – p = p
As we know,
Here, P = p, r = 6 , t = ? and I = p
yr
Question 8.
Mannan Miyan observed, after 6 years of taking a loan of some money, that the interest to be paid had become 
th of its principal. Let us determine the rate of simple interest in percent per annum.
Answer:
Let’s loan taken by Mannan Miyan was = p
So, the interest paid becomes = 
As we know,
Here, P = p, r = ?, t = 6 yr and 
Hence, the rate of simple interest in percent per annum is 
.
Question 9.
An agricultural Co-operative society gives agricultural loan to its members at the rate of simple interest of 4% per annum. But an interest is to be given at the rate of simple interest of 7.4% per annum for a loan taken from the bank. If a farmer being a member of the Co-operative society takes a loan of ₹5000 from it instead of taking loan from the bank, the let us write, by calculating the money to be saved as interest per annum.
Answer:
When farmer takes loan from agricultural society:
P = Rs. 5000, r = 4, t = 1 and I = ?
As we know,
⇒ I = Rs. 200
When a farmer takes loan from the bank:
P = Rs. 5000, r = 7.4, t = 1 and I = ?
As we know,
⇒ I = Rs. 370
Hence, the money saved by farmer
= Interest(when loan is taken from bank) – Interest(from agricultural society)
⇒ 370 – 200 = Rs. 170
Hence, money saved by farmer = Rs. 270
Question 10.
If the interest of ₹292 in 1 day be 1 paise, then let us write by calculating, the rate of simple interest in percent per annum.
Answer:
P = Rs. 292, r = ?, t = 
yr and I = Rs. .01
As we know,
Hence, the rate of simple interest per annum is 1.25.
Question 11.
Let us write, by calculating the number of yrs. for which the interest of ₹600 at the rate of simple interest of 8% per annum will be ₹168.
Answer:
P = Rs. 600, r = 8, t = ? and I = Rs. 168
As we know,
yr
Hence, The number years are 3.5
Question 12.
If I get ₹1200 return as amount (principal along with interest) by depositing ₹800in the bankat the rate of simple interest of 10% per annum, then let us write by calculating, the time for which the money was deposited in the bank.
Answer:
Interest = Amount – Principal
⇒ Interest = Rs. 1200 – Rs. 800
⇒ Interest = Rs. 400
P = Rs. 800, r = 10, t = ? and I = Rs. 400
As we know,
Hence, for 5 yr money was deposited in the bank.
Question 13.
At the same rate of simple interest in percent per annum, if a principal becomes the amount of ₹7100 in 7 yrs. and of ₹6200 in 4 yrs., let us determine the principal and rate of simple interest in percent per annum.
Answer:
Case 1:
Amount = Principal + Interest
P = p, r = ?, t = 7 yrs and I = I
As we know,
⇒ Rs. 7100 
Case 2:
P = p, r = ?, t = 4 yrs and I = I
As we know,
Amount = Principal + Interest
⇒ Rs. 6200 = p + 
Dividing the above equations we get,
⇒ 7100 + 284r = 6200 + 434r
⇒ 900 = 150r
To find the value of principal putting the value of r in any equation
⇒7100 = 
⇒ p = 
= Rs. 5000
Question 14.
Amal Roy deposits ₹2000 in the bank and Poshupoti Ghosh deposits ₹2000 in the post office at the same time. After 3 yrs. they get the return amounts ₹2360 and ₹2480 respectively. Let us write by calculating, the ratio of the rate of simple interest in percent per annum in the bank and that of in the post office.
Answer:
Case 1:
Interest = Amount – Principal
⇒ Interest = 2360 – 2000 = Rs. 360
P = Rs. 2000, R = ?, t = 3, I = Rs. 360
As we know,
⇒ R = 6
Case 2:
Interest = Amount – Principal
⇒ Interest = 2480 – 2000 = Rs. 480
As we know,
⇒ r = 8
Hence, the ratio of the rate of simple interest per annum in bank to the post office
Question 15.
A weaver Cooperative society takes a loan of ₹15,000 at the time of buying a power loom. After 5 yrs. the society has to repay ₹22125 for recovering the loan. Let us determine the rate of simple interest in percent per annum.
Answer:
Interest = Amount – Principle
⇒ I = Rs. 22125 – Rs. 15000
⇒ I = Rs. 7125
P = Rs. 15000, r = ?, t = 5 yrs and I = Rs. 7125
As we know,
⇒ r = 9.5
Hence, rate of simple interest per annum is 9.5%.
Question 16.
Aslamchacha got ₹1,00,00 when he retired from his service. He deposited some of that money in the bank and rest of his money in the post office and got ₹5400 in total per year as interest. If the rates of simple interest per annum in the and in the post office are 5% and 6%, respectively, then us write by calculating, the money he had deposited in the bank and post office.
Answer:
Case 1: Money deposited in bank
P = 10000 - p, r = 5, t = 1 and I = ?
As we know,
Case 2:For money deposited in the post-office
P = p, r = 6, t = 1 and I = ?
As we know,
From question, the total interest is
= Interest from bank + Interest from post-office
⇒ 540000 = -5p + 50000 + 6p
⇒ p = Rs 49,000
Question 17.
Rekhadidi deposited ₹10,000 of her savings in two separate banks at the same time. The rate of simple interest per annum is of 6% in one bank and that of 7% in other bank; after 2 yrs., if she gets ₹1280 in total as interest, then let us writhe by calculating, the money she had deposited separately in each of two banks.
Answer:
Case 1: For money deposited in first bank
P = p, r = 6, t = 2 and I = ?
As we know,
Case 2: For money deposited in second bank
P = 10000 – p, r = 7, t = 2 and I = ?
As we know,
From question the total interest is Rs. 1280
⇒ 1280 = 
⇒ 128000 = 12p + 140000 – 14p
⇒ 2p = 140000 – 128000
Money deposited in Second bank = 10000 – p
= 10000 – 6000 = Rs. 4000
Hence, she deposited Rs. 6000 in first bank and Rs. 4000 in another bank.
Question 18.
A bank gives 5% simple interest per annum. In the bank, Dipubabu deposits₹ 15,000 at the beginning of the year, but withdraws ₹3000 after 3 months and then again, ater 3 months he deposits ₹8000. Let us determine the amount (Principalalong with interest) Dipubabu will get at the end of the year.
Answer:
P = Rs. 15000, r = 5, t = 
yr and I = ?
Since, 
Amount = Principal + Interest
Amount = 15000 + 187.5 = Rs. 15187.5
But, after 3 months Dipubabu withdraws Rs. 3000
So, remain amount in the bank = 15187.5 – 3000 = Rs. 12187.5
P = Rs. 12187.5, r = 5, t = yr and I = ?
Since,
⇒ I = Rs. 152.34
Amount = Principal + Interest
Amount = 12187.5 + 152.34 = Rs. 12339.84
But, after 3 months Dipababu deposits Rs. Rs. 8000
So, amount become in bank = 12339.84 + 8000 = Rs. 20339.84
P = Rs. 20339.84, r = 5, t = 
and I = ?
Since,
⇒ I = Rs. 508.496
Amount (Principal along with Interest) = Principal + Interest
⇒ Amount = 20339.84 + 508.496 = Rs. 20848.336
Hence, He will get Rs. 20848.336 in the end of year.
Question 19.
Rahamatchacha takes a loan amount of ₹2,40,000 from a bank for constructing a building at the rate of simple interest of 12% per annum. After 1 yr. Of taking the loan he rents the house at the rate of ₹5200 per month. Let us determine the number of yrs. he would take to repay his loan along with interest from the income of the houserent.
Answer:
After 1 yr loan becomes
P = Rs. 240000, r = 12, t = 1 and I = ?
Since,
⇒ I = Rs. 28,800
Thus, amount becomes after n yr is
Amount = Principal + n× Intertest
⇒ Amount = 240000 + n× 28800 = Rs. (240000 + 28800n)
He rents the house at the rate of Rs. 5200 per month
n years = 12×n months
The earns rent = 5200×12×n = 62400×n
⇒ 62400n = (240000 + 28800n)
⇒ (62400 - 28800)n = 240000
⇒ n = 
Hence, he will take 
years for to repay his loan along with interest.
Question 20.
Rothinbabu deposits the money for each of his two daughters in such a way that when the ages of each of his daughters will be 18yrs. each one will get ₹1,20,000. The rate of simple interest per annum in the bank is 10% and the present ages of his daughters are 13yrs. and 8 yrs. respectively. Let us determine the money, he had deposited separately inthe bank for each of his daughters.
Answer:
Let’s money deposited by Rothinbabu for his daughters are ‘p’ and ‘P’ respectively.
For a girl of 13 years:
P = p, r = 10, t = 5 and I = ?
Since,
⇒ Amount = p + 
⇒120000 = p(
)
⇒ p = Rs. 80000
For a girl of 8 years:
P = P, r = 10, t = 10 and I = ?
Since,
⇒ Amount = p + p = 2p
⇒ 120000 = 2p
⇒ P = 
Hence, money deposited by the main for his daughters are Rs. 80000 and Rs. 60000 respectively.
Question 21.
If the interest of ₹p at the rate of simple interest of r% per annum in t years is I,then
A. I = Prt
B. PrtI = 100
C. Prt = 100 x I
D. None of these
Answer:
As we know,
Using cross-multiplication we get,
Hence option C is right.
Question 22.
A principal becomes twice of its amount in 20 yrs at a certain rate of simpleinterest. At the same rate of simple interest, that principal becomes thrice of its amount in
A. 30yrs.
B. 35yrs.
C. 40yrs.
D. 45yrs.
Answer:
Amount = 2p, Principal = p, r = r, t = 20 yr
Interest = Amount – Principal = 2p – p = p
Since,
Amount = 3p, Principal = p
⇒ Interest = 3p – p = 2p
P = p , r = 5 , t = ? and I = 2p
Since,
yr
Hence, (C) is correct option.
Question 23.
If a principal becomes twice of its amount in 10 yrs, the rate of simple interest per annum is
A. 5%
B. 10%
C. 15%
D. 20%
Answer:
Amount = 2p, Principal = p, Interest = ?
Interest = 2p – p = p
P = p, r = ?, t = 10 and I = p
Since,
⇒ r = 10 %
Question 24.
If the total interest becomes ₹ x for any principal having the rate of simple interest of x% per annum for x years then the principal will be
A. ₹ x
B. ₹100x
C. ₹
D. 
Answer:
Let’s Principle is Rs. ‘p’
P = p, r = x, t = x and I = x
Since, 
P = Rs. 
Question 25.
The total interest of a principal in n yrs. at the rate of simple interest of r% per annum in 
, the principal will be
A. ₹2p
B. ₹4p
C. ₹
D. ₹
Answer:
Let’s Principal is ‘P’
P = P, r = r , t = n and I = 
Since, 
⇒ P = 4p
Hence, (B) is correct option.
Question 26.
Let us write, whether the following statements are true or false:
(i) A man takes a loan is called debtor
(ii) If the principal and the rate of simple interest in percent per annum be constants, then the total interest and the time are inverse relation.
Answer:
(i) True
NOTE: The person or organization who gives money as loan, is called creditor and the person or organization who takes money as loan is called ‘debtor’.
(ii) False
Since,
If Principal and rate are constant then
Interest will be directly proportional to time.
Question 27.
Let us fill in the blanks:
(i) A man who gives a loan is called___________.
(ii) The amount of ₹2p in t yrs. at the rate of simple interest of 
% per annum is ₹(2p + ________).
(iii) The ratio of the principal and the amount (principal along with interest) in 1 yr. is8:9, the rate of simple interest per annum is ________.
Answer:
(i) Creditor.
(ii)
P = 2p, r = 
, t = t and I = ?
Since, 
Hence, Amount = 2p + 
(iii) 12.5%
Since, Interest = Amount – Principal
⇒ I = 
As we know,
⇒ r = 12.5%
Question 28.
Let us write the number of yrs. for which a principal becomes twice of its amount having the rate of simple interest of 
% per annum.
Answer:
Let’s assume Principal is ‘P’
Interest = Amount – Principal
Interest = 2P – P = P
P = P, r = , t = ? and I = P
Since,
⇒ t = 8 years
Hence, the number of years is 8.
Question 29.
The rate of simple interest per annum reduces 4% to 
% and for this, Amalbabu’s annual income decreases by ₹60. Let us determine Amal babu’s principal.
Answer:
Let’s assume Amal babu ‘s Principal was ‘p’
When the rate of simple interest was 4%
P = ‘P’, r = 4, t = 1 and I = ?
Since,
When the rate of simple rate is 
%
Using
According to question,
Annual income of Amal babu decreases by Rs. 60
⇒ P = Rs. 24000
Hence, Amal babu Principal was Rs. 24000
Question 30.
What is the rate of simple interest per annum, when the interest of some money in 4 yrs. will be 
part of its principal-le us determine it.
Answer:
Say, rate of simple interest per annum is ‘r’
Interest in 4 years will be = 
Let’s say Principal be ‘P’
⇒ Interest = 
P = P, r = r, t = 4 and I =
As we know,
⇒ r = 8%
Hence, rate of simple interest will be 8%.
Question 31.
What is the rate of simple interest per annum, when the interest of some money in 10yrs. will be 
part of its amount (principal along with interest)-Let us determine it.
Answer:
Say rate of simple interest per annum is ‘r’
Given: Interest of some money will be 
Let’s Principal be ‘P’
⇒ Interest = 
P = P, r = r, t = 10 years and I =
Since,
⇒ r = 4%
Question 32.
Let us determine the money for which monthly interest is ₹1 having the rate of simple interest of 5% per annum.
Answer:
Let’s assume The Principal is Rs. ‘P’
P = P, r = 5, t = year and I = Rs. 1
As we know,
⇒ P = Rs. 240