A certain sum of money, invested with simple interest, amounts to Rs.756 in 2 years and to Rs.873 in 3.5 years. Find the sum (in Rs.).

Correct option is C

Given:

The amount after 2 years = Rs. 756.

The amount after 3.5 years = Rs. 873

Principal = ?

Formula Used: 

Amount = Principal - Simple interest  

Simple interest for every year remains same .

Solution:

The difference in the amounts after 3.5 years and 2 years is:

873 − 756 = 117

This Rs. 117 is the interest earned during the 1.5 years (from 2 years to 3.5 years).

Since Rs. 117 is the interest for 1.5 years, the interest for 1 year would be:

​$$\frac{117}{1.5} = 78$$ 

So, the interest earned in 1 year is Rs. 78.

Now, we know that Rs. 78 is the interest for 1 year. 

The interest for 2 years is:

Interest for 2 years = 78 × 2= 156

The amount after 2 years is Rs. 756, so the principal is:

Principal = 756 − 156 = 600 

Thus the principal sum is Rs. 600.