Amala, Bina, and Gouri invest money in the ratio 3 : 4 : 5 in fixed deposits…

Concept: When the same set of entities has two different ratios describing them — here, the ratio of amounts invested and the ratio of annual interest rates — the ratio of the resulting product quantity (interest income = investment × rate) is found by multiplying the corresponding terms of the two ratios. Once a combined ratio is known, if the actual difference between any two parts is given, dividing it by the difference in ratio units gives the value of one unit, which can then be scaled to find the total.

Application:

1. Investment ratio (Amala : Bina : Gouri) = 3 : 4 : 5

2. Annual interest rate ratio (same order) = 6 : 5 : 4

3. Interest income is proportional to investment × rate, so income ratio = (3×6) : (4×5) : (5×4) = 18 : 20 : 20

4. Bina's income − Amala's income = 20 − 18 = 2 parts = Rs 250, so 1 part = Rs 125

5. Total interest income = sum of all parts × value of 1 part = (18 + 20 + 20) × 125 = 58 × 125 = Rs 7250

Cross-check: Substituting back: Amala's income = 18 × 125 = Rs 2250, Bina's income = 20 × 125 = Rs 2500, Gouri's income = 20 × 125 = Rs 2500. Bina's income exceeds Amala's by 2500 − 2250 = Rs 250, matching the given condition, and the total 2250 + 2500 + 2500 = Rs 7250 confirms the result.