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

Answer 1

The correct option is A 450 Rupees, 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 3years - 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
=522-72
= ₹ 450 rupees = x
We know Interest for 1 year = ₹ 36 ; P = ₹ 450 and T = 1 year
$36=\frac{450\times 1\times R}{100}$

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

$R=8$%
Hence the sum is ₹ 450 and rate of interest is 8%.