A lends a sum of money for 10 years at 5% SI. B lends double the amount for 5 years

Ques - A lends a sum of money for 10 years at 5% SI. B lends double the amount for 5 years at the same rate of interest. Which of the following statements is true in this regard?

(a) A will get twice the amount of interest that B would get.

(b) B will get twice the amount of interest that A would get.

(c) A will get the same amount of interest that B would get.

(d) B will get four times the amount of interest that A would get.

Solution - 

Given,

For A,

P = x

T = 10 years

R = 5%

So,

S.I. = (P×R×T) / 100

S.I. = (X × 5 × 10) / 100

S.I. = (50X) / 100

S.I. = X/2

Now,

For B,

P = 2x

T =5 years

R = 5%

So,

S.I. = (P×R×T) / 100

S.I. = (2X × 5 × 5) / 100

S.I. = (50X) / 100

S.I. = X/2

Thus,

Simple interest will be same for both (X/2).

Therefore,

A will get the same amount of interest that B would get.

Hence,

The correct answer is option (c) A will get the same amount of interest that B would get.

Thank You