Question

A certain sum becomes 2356 in 3 years and 2660 in 5 years on simple interest. What is the value of the sum?

• A. 1800
• B. 1880
• C. 1900
• D. 1980

Answer 1

The Correct Option is C

Let the principal sum be \(P\) and the simple interest rate be \(r\). We are given that after 3 years, the sum becomes ₹2356 and after 5 years, it becomes ₹2660.

So, \(P + 3rP = 2356\) and \(P + 5rP = 2660\).

Subtracting the first equation from the second, we get \(2rP = 2660 - 2356 = 304\). So \(rP = \frac{304}{2} = 152\).

Substituting \(rP = 152\) into the first equation, we get \(P + 3(152) = 2356\).

\(P + 456 = 2356\)

\(P = 2356 - 456 = 1900\)

Answer 2

The difference in interest for two years is $2660 - 2356 = 304$, 

So the interest for 1 year is 152. 

The interest for 3 years is $152 \times 3 = 456$. 

The principal is $2356 - 456 = 1900$.