Question

A certain sum of money amounts to ₹ 522 rupees in 2 years and ₹558 rupees in 3 years lent at simple interest. Find the sum and rate of interest.

• A. ₹ 550 , 8%
• B. ₹ 350, 5%
• C. ₹ 450, 8%
• D. ₹ 400 , 5%

Answer 1

The correct option is C ₹ 450, 8%

Let the sum/principal be x
Let the rate of interest be r
Amount after 2 years = ₹ 522
Amount after 3 years = ₹ 558

Hence, the interest for 1 year
= Amount after 3 years - Amount after 2 years
= ₹ 558 - ₹ 522 = ₹ 36

₹ 36 is the interest for 1 year
For 2 years the interest is $2\times 36=72$

Principle = Amount after 2 years - Interest for 2 years
x = ₹ (522-72)
x = ₹ 450

We know,
Interest for 1 year = ₹ 36 ; P = ₹ 450 and T = 1 year
Using SI formula:
$SI=\frac{P\times R\times T}{100}$

$⟹$ $36=\frac{450\times 1\times R}{100}$

$⟹$$R=\frac{36\times 100}{450}$

$⟹$$R=8$%

Hence, the sum is ₹ 450 and rate of interest is 8%.