Question 1

A sum of money amounts to ₹ 2240 at 4% per annum simple interest in 3 yr. The interest on the same sum for 6 months at 3.5% per annum is

Accepted Answer

If the sum be ₹ P, then (2240 - P) = (P x 4 x 3)/100 ⇒ 2240 = 12P/100 + P ⇒ 2240 = 112P/100 ∴ P = (2240 x 100)/112 = ₹ 2000 Now, required interest, SI = PRT/100 = [{2000 x (7/2) x (1/2)} /100] = ₹ 35

Question 2

The simple interest on a sum of money at 9% per annum for 5 yr is half the sum. What is the sum?

Accepted Answer

Let the sum be P. ∵ SI = P/2 ∴ P/2 = (P x 9 x 5)/100 Clearly data is inadequate.

Question 3

The simple interest on a sum of money at 8% per annum for 6 yr is half the sum. What is the sum?

Accepted Answer

Let sum = P Then, according to the question. SI = P/2 ∴ P/2 = (P x 8 x 6)/100 ∴ It is clear that data is inadequate.

Question 4

A sum was put at simple interest at a certain rate for 2 years . Had it been put at 3% higher rate, it would have fetched Rs 300 more. The sum is

Accepted Answer

Let the sum be P. And the original rate be y% per annum. Then new rate=(y+3)% per annum According to question, [(P × (y+3) × 2)/100]=[(P × y × 2)/100]=300 ∴ [(Py + 3P)/100]=[Py/100] = 150 ∴ Py+ 3P - Py=15000 ∴ 3P=15000 ∴ P= 5000 Thus, the sum is Rs 5000

Question 5

The simple interest on a sum of money at 10% per annum for 6 year is half the sum. Then, the sum is?

Accepted Answer

Let the sum be Rs 'y' Since Simple Interest = Rs ( y / 2) and, T = 6 yr , R = 10% per annum So Simple Interest, SI = (P x R x T)/100 where, R = Rate T = Time SI= Simple Interest now, According to problem, ( y / 2 ) = ( y x 10 x 6)/100 ⇒ (1/2)=(6/10) ⇒ which is not true, so it is not a possible case.

Question 6

The simple interest at x% for x years will be Rs x on a sum of ....

Accepted Answer

As Sum = [(100 x SI)/(Time x Rate)] here, let R =x%, T=x yr, and, SI=Rs x ∴ Sum=[(100 × x)/(x × x)] =(100/x)

Question 7

A certain sum lent out at simple interest amounts to Rs 575 in 3 yr and to Rs 625 in 5 yr. Then the rate of interest is?

Accepted Answer

Let the sum be Rs 'y' and , rate of interest = R% Simple Interest for 2 yr =Rs( 625 - 575 ) = Rs 50 ∴ Sum of money, y=Rs( 575 - 75)= Rs 500 ∴ R= [(100 x SI)/(Sum x Time)] =[(100x 75)/(500 x 3)]=5 %

Question 8

The simple interest on a sum of money is 1/9 of the principle and the number of years is equal to the rate percent annum. The rate percent annum is?

Accepted Answer

Let principle = Rs. P Then S.I = P/9 Let Rate = R% per annum and time = R years Then, as we know SI = (P x R x T) / 100. ⇒ P/9 = ( P x R x R) / 100 ⇒ R2 = 100/9 ∴ R = 10/3 = 31/3 % per annum

Question 9

A moneylender finds that due to a fall in the rate of interest from 13% to 12 1/ 2% his yearly income diminishes by Rs. 104. His capital is?

Accepted Answer

Let capital = Rs . P Then, SI1 - SI2 = 104. ⇒ (P x 13 x 1)/100 - (P x 25/2 x 1) /100 = 104 ⇒ 13P/100 - P/8 = 104 ⇒ 26P -25P = (104 x 200) ⇒ P = 20800 ∴ Capital = Rs. 20800

Question 10

A man invested 1/3 of his capital at 7%, 1/4 at 8% and remainder at 10%. If his annual income is Rs. 561, the capital is?

Accepted Answer

Let the capital be Rs. P, then (P/3) x (7/ 100) + (x/4) x (8/100) + [P - (P/3 + P/4)] x 10/100 = 561 ⇒ 7P/300 + P/50 + P/24 = 561 ⇒ 42P + 36P + 75P = 1009800 P = 1009800/153 = 6600

Question 11

A certain sum of money at simple interest amounts to Rs. 1260 in 2 years and to Rs. 1350 in 5 years. The rate per cent per annum is?

Accepted Answer

S.I for 3 years = Rs. (1350 - 1260) = Rs. 90 S.I for 2 years = Rs.(90/3) x 2 = Rs . 60 ∴ Sum = Rs. (1260 - 60) = Rs. 1200 ∴ Rate = (100 x SI) / (P x T) = (100 x 60) / (1200 x 2) = 2.5%

Question 12

A lent Rs. 600 to B for 2 years and Rs. 150 to C for 4 years and received altogether from both Rs. 90 as simple interest. The rate of interest is?

Accepted Answer

Let rate = R% per annum. Then, [(600 x R x 2)/ 100 ] + [(150 x R x 4 ) / 100] = 90 ⇒ 18R = 90 ∴ R = 5%

Question 13

Rs. 800 amounts to Rs. 920 in 3 years at simple interest. If the interest rate is increased by 3% It would amount to how much?

Accepted Answer

Principal = Rs. 800 S.I. = Rs. (920 - 800) = Rs. 120 and Time = 3 years ∴ Original rate = (100 x SI) / (P x T) = (100 x 120) / ( 800 x 3) = 5% New rate = 8% Now, S.I . = Rs.(800 x 8 x 3) /100 = Rs. 192 ∴ Amount = Rs. (800 + 192) = Rs. 992

Question 14

The simple interest on a sum of money at 8% per annum for 6 years is half the sum. The sum is?

Accepted Answer

Let, Sum = P Then S.I = P/2 Rate = 8% and Time = 6 years But P/2 = (P x 8 x 6) /100 (Not possible ) Thus, data is inadequate.

Question 15

If the interest on Rs. 1200 be more than the interest on Rs. 1000 by Rs. 50 in 3 years, the rate per cent is?

Accepted Answer

Let rate = R% per annum. Then, (1200 x R x 3)/100 - (1000 x R x 3)/100 = 50 ⇒ 6R = 50 ⇒ R = 81/3 ∴ Rate = 81/3% per annum

Question 16

In how many years will a sum of money double itself at 12% per annum?

Accepted Answer

Let principal = P. Then, S.I = P, Rate (R) = 12% Time = (100 x SI) / (R x P) = (100 x P) / (P x 12) years = 25/3 years = 8 years 4 months

Question 17

A sum was put at simple interest at a certain rate for 2 years. Had it been put at 1% higher rate, it would have fetched Rs. 24 more, The sum is?

Accepted Answer

Let sum = P and original rate = R% per annum Then, [(P x (R + 1) x 2)/100] - [(P x R x 2)/100] = 24 ⇒ P = 1200

Question 18

A sum money becomes (8/5) of itself in 5 years at a certain rate of interest . The rate percent per annum is?

Accepted Answer

Let sum = Rs. P. Then amount = Rs. (8P/5) ∴ S.I = Rs. (8P/5 - P ) = Rs.(3P/5) ∴ Required rate = (100 x SI) / (P x T) = [(100 x 3P/5) / (P x 5)]% = 12%

Question 19

The difference between the interest received from two different bank on Rs. 500 for 2 year is Rs. 2.50. The difference between their rates is?

Accepted Answer

Let the rates be R1% and R2%. Then, (500 x R1 x 2)/ 100 - (500 x R2 x 2)/ 100 = 2.5 ⇒ 10(R1 - R2) = 2.5 ∴ Req difference = R1 - R2 = 0.25%

Question 20

A certain sum of money at simple interest amounts to Rs. 1012 in 2 1/ 2 years and to Rs. 1067.20 in 4 years. The rate of interest per annum is?

Accepted Answer

∵ S.I. for 3/2 years = Rs. (1067.20 - 1012) = Rs. 55.20 ⇒ S.I. for 5/2 years = Rs. 55.20 x (2/3) x (5/2) = 92 ∴ Sum = Rs. (1012 - 92) = Rs.920 Hence, Rate = (100 x SI)/(P x T) = (100 x 92) / (920 x 5/2 ) = 4%

Simple Interest Questions