A certain sum of money amounts to Rs. 2,500 in a span of 5 years and further…

Step-by-Step Solution

To find the principal sum, we use the fact that in simple interest, the interest earned each year is constant.

1. Calculate the interest over the two-year period:

   • Amount after 7 years = Rs. 3,000

   • Amount after 5 years = Rs. 2,500

   • The difference represents the simple interest earned over 2 years (7 - 5 = 2 years).

   • Interest for 2 years = 3000 - 2500 = Rs. 500.

2. Calculate the interest for 1 year:

   • Interest for 1 year = 500 / 2 = Rs. 250.

3. Find the principal:

   • Interest for 5 years = 250 * 5 = Rs. 1,250.

   • Since Amount = Principal + Interest, then Principal = Amount after 5 years - Interest for 5 years.

   • Principal = 2500 - 1250 = Rs. 1,250.