Question 1

A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?

Accepted Answer

S.I. = Rs. (15500 - 12500) = Rs. 3000. Rate = ❨ 100 x 3000 ❩% = 6% 12500 x 4

Question 2

Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?

Accepted Answer

Let rate = R% and time = R years. Then, ❨ 1200 x R x R ❩ = 432 100 ⟹ 12R2 = 432 ⟹ R2 = 36 ⟹ R = 6.

Question 3

How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?

Accepted Answer

Time = ❨ 100 x 81 ❩years = 4 years. 450 x 4.5

Question 4

A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?

Accepted Answer

Principal = Rs. ❨ 100 x 4016.25 ❩ 9 x 5 = Rs. ❨ 401625 ❩ 45 = Rs. 8925.

Question 5

A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:

Accepted Answer

S.I. for 1 year = Rs. (854 - 815) = Rs. 39. S.I. for 3 years = Rs.(39 x 3) = Rs. 117. ∴ Principal = Rs. (815 - 117) = Rs. 698.

Question 6

A sum of money amounts to Rs. 9800 after 5 years and Rs. 12005 after 8 years at the same rate of simple interest. The rate of interest per annum is:

Accepted Answer

S.I. for 3 years = Rs. (12005 - 9800) = Rs. 2205. S.I. for 5 years = Rs. ❨ 2205 x 5 ❩ = Rs. 3675 3 ∴ Principal = Rs. (9800 - 3675) = Rs. 6125. Hence, rate = ❨ 100 x 3675 ❩% = 12% 6125 x 5

Question 7

Mr. Thomas invested an amount of Rs. 13,900 divided in two different schemes A and B at the simple interest rate of 14% p.a. and 11% p.a. respectively. If the total amount of simple interest earned in 2 years be Rs. 3508, what was the amount investe…

Accepted Answer

Let the sum invested in Scheme A be Rs. x and that in Scheme B be Rs. (13900 - x ). Then, ❨ x x 14 x 2 ❩ + ❨ (13900 - x) x 11 x 2 ❩ = 3508 100 100 ⟹ 28x - 22x = 350800 - (13900 x 22) ⟹ 6x = 45000 ⟹ x = 7500. So, sum invested in Scheme B = Rs. (13900 - 7500) = Rs. 6400.

Question 8

A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years on simple interest at the same rate of interest and received Rs. 2200 in all from both of them as interest. The rate of interest per annum is:

Accepted Answer

Let the rate be R% p.a. Then, ❨ 5000 x R x 2 ❩ + ❨ 3000 x R x 4 ❩ = 2200. 100 100 ⟹ 100R + 120R = 2200 ⟹ R = ❨ 2200 ❩ = 10. 220 ∴ Rate = 10%.

Question 9

An automobile financier claims to be lending money at simple interest, but he includes the interest every six months for calculating the principal. If he is charging an interest of 10%, the effective rate of interest becomes:

Accepted Answer

Let the sum be Rs. 100. Then, S.I. for first 6 months = Rs. ❨ 100 x 10 x 1 ❩ = Rs. 5 100 x 2 S.I. for last 6 months = Rs. ❨ 105 x 10 x 1 ❩ = Rs. 5.25 100 x 2 So, amount at the end of 1 year = Rs. (100 + 5 + 5.25) = Rs. 110.25 ∴ Effective rate = (110.25 - 100) = 10.25%

Question 10

A man took loan from a bank at the rate of 12% p.a. simple interest. After 3 years he had to pay Rs. 5400 interest only for the period. The principal amount borrowed by him was:

Accepted Answer

Principal = Rs. ❨ 100 x 5400 ❩ = Rs. 15000. 12 x 3

Question 11

A sum of Rs. 725 is lent in the beginning of a year at a certain rate of interest. After 8 months, a sum of Rs. 362.50 more is lent but at the rate twice the former. At the end of the year, Rs. 33.50 is earned as interest from both the loans. What w…

Accepted Answer

Let the original rate be R%. Then, new rate = (2R)%. Note: Here, original rate is for 1 year(s); the new rate is for only 4 months i.e. ⅓ year(s). ∴ ❨ 725 x R x 1 ❩ + ❨ 362.50 x 2R x 1 ❩ = 33.50 100 100 x 3 ⟹ (2175 + 725) R = 33.50 x 100 x 3 ⟹ (2175 + 725) R = 10050 ⟹ (2900)R = 10050 ⟹ R = 10050 = 3.46 2900 ∴ Original rate = 3.46%

Question 12

A certain amount earns simple interest of Rs. 1750 after 7 years. Had the interest been 2% more, how much more interest would it have earned?

Accepted Answer

We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate.

Question 13

A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lends it to another person at 6¼% p.a for 2 years. Find his gain in the transaction per year.

Accepted Answer

Gain in 2 years = Rs. [ ❨ 5000 x 25 x 2 ❩ - ❨ 5000 x 4 x 2 ❩ ] 4 100 100 = Rs. (625 - 400) = Rs. 225. ∴ Gain in 1 year = Rs. ❨ 225 ❩ = Rs. 112.50 2

Question 14

What will be the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years?

Accepted Answer

Let the principal be P and rate of interest be R%. ∴ Required ratio = ❨ P x R x 6 ❩ 100 = 6PR = 6 = 2 : 3. ❨ P x R x 9 ❩ 100 9PR 9

Question 15

The sum required to earn a monthly interest of Rs 400 at 10 % per annum at simple interest is

Accepted Answer

Total interest needed in a year = Rs 400 × 12 = Rs 4800 Principal = (100 × SI)/R × T where, R = Rate T = Time SI= Simple Interest

Question 16

In what time will the simple interest on Rs 400 at 10% per annum be the same as the simple interest on Rs 1000 for 4 year at 4 % per annum?

Accepted Answer

Here , P= Rs 1000 T= 4 yrs R= 4 % where, P= Principal T= Time R= Rate Since , Simple Interest on Rs 1000=(1000 × 4 × 4)/100 = Rs 160 now, simple interest=Rs 160 P = Rs 400 R = 10 % then, T=(100 × SI)/P × R = (100 × 160)/(400 × 10) = 4 yr

Question 17

At what rate percent per annum will a sum of money double in 8 yr?

Accepted Answer

Let Sum = P, Then SI=P As Amount A = 2 × P where , P = Principal Rate R = (100 × SI)/(P × T) = (100 × P)/(P × 8) % = 12.5 % where , SI= Simple Interest T= Time

Question 18

The amount instalment will discharge on debit of Rs 3220 due in 4 year at 10 % simple interest?

Accepted Answer

Let the amount instalment be Rs ' x ' Then According to question, (Amount of 'x' for 3 yrs) + (Amount of 'x' for 2 yrs) + (Amount of 'x' for 1 yrs) + x =3220 or, [x+(x × 10 × 3)/100] + [x+(x × 10 × 2)/100] + [x+(x × 10 × 1)/100] + x=3220 ⇒ 4x+ (30x/100)+(20x/100)+(10x/100)=3220 ⇒ 460x=322000 ⇒ x=Rs 700 ∴ Each Instalment= Rs 700

Question 19

A certain sum amounts to Rs 1586 in 2 year and Rs 1729 in 3 year. Find the rate and the sum.

Accepted Answer

Simple Interest in 1 year= Rs (1729 - 1586) = Rs 143 now, SI in 2 year = Rs 286 Principal P= Rs(1586 - 286) = 1300 And R= (100 × SI)/(P × T) = (100 × 143)/(1300 × 1) = 11 % where, R = rate SI= Simple Interest P = Principal T= Time

Question 20

Find the sum of money will amount to Rs 900 in 4 years at 5 % per annum on simple interest?

Accepted Answer

Let the sum of money be Rs y So Amount = y +[( y x 5 x 4 )/100] But Amount = Rs 900 ⇒ 900 = y +(20y)/100 ⇒ 900 = 6y / 5 ⇒ y = ( 900 x 5) /6 = Rs 750

Simple Interest Questions