In how many minimum number of complete years will the interest on Rs. 212.50…

CONCEPT: Simple Interest is SI = (P × R × T)/100. For a fixed principal P and rate R, the interest earned per year is the constant P×R/100. Over T years the total interest is T times that constant, so the total is a whole number of rupees exactly when T, multiplied by the per-year fraction in its lowest terms, clears the denominator — i.e. T must be a multiple of that denominator.

APPLICATION: Here P = Rs. 212.50 and R = 3% per annum, so the interest earned per year is 212.50 × 3/100 = 6.375 = 51/8 rupees. Since 51 and 8 share no common factor, T × 51/8 is a whole number only when T is a multiple of 8.

Checking the offered durations against this rule:

1. For 6 years: 6 × 51/8 = 38.25 (not an integer).

2. For 7 years: 7 × 51/8 = 44.625 (not an integer).

3. For 8 years: 8 × 51/8 = 51 (an integer).

4. For 9 years: 9 × 51/8 = 57.375 (not an integer).

CROSS-CHECK: Applying the direct formula for 8 years, SI = (212.50 × 8 × 3)/100 = 5100/100 = Rs. 51, confirming the fraction-based result. Since 8 is the smallest positive multiple of 8, it is also the minimum number of complete years for which the interest is an exact number of rupees.

∴ The required answer is 8 years.