Question 1

At the rate of 8 1/ 2% per annum simple interest, a sum of ₹ 5800 will earn how much interest in 2 yr 3 months?

Accepted Answer

Time = 2 yr 3 months = 21/4 yr = 9/4 yr ∴ SI = [5800 x (17/2) x (9/4)] / 100 = 8874/8 = ₹ 1109.25 = ₹ 1109

Question 2

A certain sum becomes 3 fold at 4% annual rate of interest. At what rate, it will become 6 fold?

Accepted Answer

Here, n = 3, m = 6, R1 = 4% ∴ R2 = [(m - 1)/(n - 1)] x R1 = [(6 - 1)/(3 - 1)] x 4 =(5/2) x 4 = 10%

Question 3

Kriya deposits an amount of ₹ 65800 to obtain a simple interest at the rate of 14% per annum for 4 yr. What total amount will Kriya get at the end of 4 yr?

Accepted Answer

Here, P = ₹ 65800, R = 14% T = 4 yr Hence, SI = (65800 x 14 x 4) / 100 =₹ 36848 ∴ Required amount = P + SI = 65800 + 36848 = ₹ 102648

Question 4

In a certain time, a sum becomes 4 times at the rate of 5% per annum. At what rate of simple interest, the same sum becomes 8 times in the same duration?

Accepted Answer

Let the sum be p Then, for R = 5% SI = (4p - p) = 3p ∴ 3p = (P x 5 x T)/100 = PT/20 ⇒ T = 60 yr Again, for another rate (R) SI = (8P - P) = 7P ∴ 7P = (P x R x 60)/100 ⇒ R = (7 x 100)/60 = 35/3% = 112/3 %

Question 5

In what time does a sum of money become four fold at the simple interest ratio of 10% per annum?

Accepted Answer

Here, n = 4, R = 10, T = ? According to the formula, R = 100 (n - 1)/T ⇒ 10 = [100(4 - 1)]/T = (100 x 3)/T ∴ T = 30 yr

Question 6

Simple interest for the sum of ₹ 1230 for 2 yr is ₹ 10 more than the simple interest for ₹ 1130 for the same duration. Find the rate of interest. `

Accepted Answer

According to the question, [(1230 x 2 x R)/100] - [(1130 x 2 x R)/100] = 10 ⇒ (200 x R)/100 = 10 ∴ R = 5%

Question 7

For a certain sum, the simple interest in 2 yr at 8% per annum is ₹ 110 more than the simple interest in 1 yr at the ratio of 5% per annum for the same sum. Find the sum.

Accepted Answer

Given, SI1 - SI2 = 110, T1 = 2 Yr, T2 = 1 yr, R1 = 8%, R2 = 5% According to the question, [(P x 8 x 2)/100] - [(P x 5 x 1)/100] = 110 ⇒ 11P/100 = 110 ∴ P = ₹ 1000

Question 8

A sum was invested for 4 yr at a certain rate of simple interest. If it had been invested at 2% more annual rate of interest, then ₹ 56 more would have been obtained. What is the sum?

Accepted Answer

According to the question [P x (R + 2) x 4]/100 - [P x R x 4]/100 = 56 ⇒ (4PR + 8P - 4PR)/100 = 56 ⇒ 8P/100 = 56 ∴ P = (56 x 100)/8 = ₹ 700

Question 9

A sum becomes 6 fold at 5% per annum. At what rate, the sum becomes 12 fold?

Accepted Answer

SI at 5% = 6P - P = 5P ∴ 5P = (P x 5 x T) /100 ⇒ T = 100 yr Now, for new rate (R), 11P = (P x R x 100)/100 ∴ R =11%

Question 10

A sum becomes two fold in 6 yr at a certain rate of interest. Find the time, in which the same mount will be 10 fold at the same rate of interest.

Accepted Answer

Here, n = 2, m =10, T1 = 6 yr, T2 = ? ∴ T2 = [(m - 1) / (n - 1)] x T1 = [(10 - 1)/(2 - 1)] x 6 = 54 yr

Question 11

The difference of simple interest from two banks for ₹ 1000 in 2 yr is ₹ 20. Find the difference in rates of interest.

Accepted Answer

Let the two rates be R1 and R2 According to the question, [(1000 x 2 x R1)/100] - [(1000 x 2 x R2)/100] = 20 ⇒ [2000 x (R1 - R2)] / 100 = 20 ∴ R1 - R2 = 20/20 = 1%

Question 12

Raju lent ₹ 400 to Ajay for 2 yr and ₹ 100 to Manoj for 4 yr and received from both ₹ 60 as collective interest, Find the rate of interest, simple interest being calculated.

Accepted Answer

Let rate is R% According to the question. [(R x 400 x 2)/100] + [(R x 100 x 4)/100] = 60 ⇒ 12R = 60 ∴ R = 60/12 = 5%

Question 13

2/3 part of my sum is lent out at 3%, 1/6 part is Lent out at 6% and remaining part is lent out 12% All the three parts are lent out at simple interest. If the annual income is ₹ 25, what is the sum?

Accepted Answer

Let entire sum = P According to the question, [(2P/3) x 3%] + [(P/6) x 6%] + [1 - ( 2/3 + 1/6 )] P x 12% = 25 ⇒ [(2P/3) x (3/100)] + [(P/6) x (6/100)] + [1 - 4 + 1/6] x (12P/100) = 25 ⇒ 2P/100 + P/100 + 2P/100 = 25 ⇒ 5P = 2500, ∴ P = 500

Question 14

Suresh borrowed ₹ 800 at 6% and Naresh borrowed ₹ 600 at 10% After how much time will they both have equal debts?

Accepted Answer

Given, R1 = 6% R2 = 10% According to the question, 800 + [(800 x 6 x T)/100] = 600 + [(600 x 10 x T)/100] 800 + 48T = 600 + 60T ⇒ 12T = 200 ⇒ 3T = 50 ∴ T = 50/3 = 162/3 yr

Question 15

A sum of ₹ 1521 lent out two parts in such a way that the interest on one part at 10% for 5 yr is equal to that of another part at 8% for 10 yr. What will be the two parts of sum?

Accepted Answer

Given, T1 = 5 yr, R1 = 10% and T2 = 10 yr, R2 = 8% Let the first part = P Then, second part = (1521 - P) Now, according to the question. [(P x 5 x 10)/100] = [{(1521 - P) x 10 x 8}/100] ⇒ 5P = 12168 - 8P ⇒ 13P = 12168 ⇒ P = ₹ 936 So second part = 1521 - 936 = ₹ 585

Question 16

Rashim lent ₹ 600 to Geeta for 2 yr and ₹ 150 to Seeta 4 yr and received altogether ₹ 80 as simple interest from both. Find the rate of interest.

Accepted Answer

Given. T1 = 2 yr and T2 = 4 yr, P1 = 600, P2 = 150. According to the question, SI1 + SI2 = 80 [(600 x R x 2)/100] + [(150 x R x 4)/100] = 80 ⇒ 120R + 60R = 800 ⇒ 180R = 800 ∴ R = 800/180 = 80/18 = 40/9 = 44/9%

Question 17

The simple interest of a sum of money is 1/144 of the principal and the number of years is equal to the rate per cent per annum. What will be the rate per cent per annum?

Accepted Answer

Let the principal be P. Then, according to the question, (P x T x T) / 100 = P/144 [∵ time and rate are equal] ⇒ T2 = 100/144 ∴ T = 10/12 = 5/6 %

Question 18

The simple interest on a sum of money is 1 / 16 of the principal and the number of years is equal to the rate per cent annum. Find the rate per cent.

Accepted Answer

Let principal = P, time = T and rate = T According to the question, (P x T x T) / 100 = P/16 [∵ time and rate are equal] ⇒ T2 = 100/16 or T = 10/4 = 5/2 = 21/2 %

Question 19

The principle on which a simple interest of ₹ 55 will be obtained after 9 months at the rate of 3 2/ 3% per annum is

Accepted Answer

Let. principal = P Given, SI = 55, Time T = 9 months = 9/12 yr, Rate R = 32/3% = 11/3 % ∴ SI = (P x R x T) / 100 ⇒ P = (100 x SI) / (R x T) ⇒ (55 x 100) / [(11 x 9) / (3 x 12)] = 2000 ∴ Principal (P) = ₹ 2000

Question 20

The simple interest on a sum of money will be ₹ 200 after 5 yr In the next 5 yr principal is tripled. What will be the total interest at the end of the 10th yr?

Accepted Answer

According to the question, SI for 5 yr = ₹ 200 ∴ Total SI for 10 yr = 200 + 600 = ₹ 800 When principal is trebled, then SI for 5 yr will also be treble and hence SI for next 5 yr will be ₹ (200 x 3) i.e., ₹ 600.

Simple Interest Questions