A sum was put at simple interest at certain rate for 3 years. Had it been put…

Simple Interest is given by SI = P × R × T / 100, where P is the principal, R is the rate of interest per annum, and T is the time in years. If the rate is increased by a fixed amount while the principal and time stay the same, the resulting EXTRA interest equals P × (rate increase) × T / 100 — this lets the principal be found directly from a known rate-difference and a known extra-interest amount, without ever needing to know the original rate.

1. Let the principal be P (in Rs.), the original rate be R% per annum, and the time be T = 3 years.

2. At the higher rate, (R + 1)% per annum, the interest earned over the same 3 years increases — the rate difference is 1 percentage point.

3. The extra interest earned equals P × 1 × 3 / 100, and this is given to be Rs. 63.

4. So P × 1 × 3 / 100 = 63.

5. Simplify the left side: 3P / 100 = 63.

6. Solve for P: P = (63 × 100) / 3 = 6300 / 3 = 2100.

Check: with P = Rs. 2100 for 3 years, a 1% rate increase gives extra interest = 2100 × 1 × 3 / 100 = Rs. 63, exactly matching the given condition. So the sum is Rs. 2100.