A certain sum of money at simple interest amounts to ₹1062 in 2 years and to…

Concept: Under simple interest, the interest earned every year is the same fixed amount (since it is always calculated on the original principal, never on previously accumulated interest). So the extra interest earned over any additional time gap is exactly proportional to the length of that gap — this lets us work out the annual interest directly from two amounts given at two different times.

Application:

1. The amount grows from ₹1062 at 2 years to ₹1183.50 at 3½ years — a gap of 1½ years. The extra interest earned in this gap is ₹1183.50 − ₹1062 = ₹121.50.

2. Since simple interest accrues at a uniform rate every year, the interest for one full year = ₹121.50 ÷ 1.5 = ₹81.

3. So the interest built up over 2 years = ₹81 × 2 = ₹162.

4. The principal is the 2-year amount minus the interest accrued by then: Principal = ₹1062 − ₹162 = ₹900.

5. Using SI = (P × R × T) / 100 with SI = ₹162, P = ₹900, T = 2 years: 162 = (900 × R × 2) / 100, which gives R = 16200 / 1800 = 9.

Cross-check: With P = ₹900 and R = 9% per annum, the interest for 3½ years = (900 × 9 × 3.5) / 100 = ₹283.50, giving an amount of ₹900 + ₹283.50 = ₹1183.50 — exactly matching the given figure, confirming the rate of 9% per annum.