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

To solve the problem, we need to determine the principal amount (P) using the information provided about simple interest over different years. We know the sum amounts to 2356 after 3 years and 2660 after 5 years. We can calculate the simple interest (SI) for each of these times and use them to find P.

1. Calculate the Simple Interest for 2 years (from year 3 to year 5):
   \[ SI_{2} = 2660 - 2356 = 304 \]
2. Since this interest is earned for 2 years, the annual interest is:
   \[ \text{Annual Interest} = \frac{304}{2} = 152 \]
3. Using the annual interest, calculate the total interest for 3 years:
   \[ SI_{3} = 3 \times 152 = 456 \]
4. Use the sum at 3 years to find the principal:\
   \[ P + SI_{3} = 2356 \]
   \[ P + 456 = 2356 \]
   \[ P = 2356 - 456 = 1900 \]

Hence, the value of the sum is 1900.

Answer 2

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 \(P + 3(152) = 2356\).

\(P + 456 = 2356\)

\(P = 2356 - 456 = 1900\)