A sum of money Rs. 40,000 is deposited for 3 years at the rate of compound…

Concept: When compound interest is charged at different rates in successive years, each year's rate is applied only to the amount carried forward from the previous year (not to the original principal). So the final amount equals Principal × (1 + rate1) × (1 + rate2) × (1 + rate3). Expressing each year's rate as a Principal : Amount ratio and multiplying the three ratios together (the unit method) gives the same result while avoiding decimal multiplication.

Applying this to the given values:

1. Principal = Rs. 40,000; the rates for the first, second and third year are 5%, 8% and 10% respectively.

2. Write each rate as a Principal : Amount ratio: 5% = 1/20 gives 20 : 21; 8% = 2/25 gives 25 : 27; 10% = 1/10 gives 10 : 11.

3. Multiply the three Principal terms together, and separately multiply the three Amount terms together: total principal units = 20 × 25 × 10 = 5000; total amount units = 21 × 27 × 11 = 6237.

4. Since 5000 units represent the actual principal of Rs. 40,000, one unit = Rs. 40,000 / 5000 = Rs. 8.

5. Amount after three years = 6237 units × Rs. 8 = Rs. 49,896.

Cross-check: This matches directly multiplying the year-on-year growth factors: 40,000 × 1.05 × 1.08 × 1.10 = 49,896, confirming the unit-method result.

So the amount after three years is Rs. 49,896.