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 determine the principal amount (P), we will analyze the simple interest accrued over different periods. The total sum is 2356 after 3 years and 2660 after 5 years. We can derive P by calculating the simple interest (SI).

1. Calculate the Simple Interest accrued between year 3 and year 5:
   \[ SI_{2} = 2660 - 2356 = 304 \]
2. Determine the annual simple interest, as this interest was earned over 2 years:
   \[ \text{Annual Interest} = \frac{304}{2} = 152 \]
3. Calculate the total simple interest accumulated over 3 years:
   \[ SI_{3} = 3 \times 152 = 456 \]
4. Find the principal amount using the sum after 3 years and the calculated interest:
   \[ P + SI_{3} = 2356 \]
   \[ P + 456 = 2356 \]
   \[ P = 2356 - 456 = 1900 \]

The principal sum is 1900.