Ratio of simple interest for different rates – UGC NET Question

Simple interest is given by SI = (P × R × T)/100, so for the same principal P, the interest is directly proportional to the product of rate and time. For the first case, the product R × T is 5 × 3 = 15; for the second, it is 8 × 2 = 16. Therefore, the ratio of the first interest to the second is 15:16.

Option A:
Option A, 3:4, might be guessed by loosely comparing 5% and 8% or the times, but it does not reflect the exact products 15 and 16. When the detailed calculation is performed, the resulting ratio is 15:16, not 3:4.

Option B:
Option B, 4:3, reverses the direction and suggests that the first interest is larger in proportion than the second, which would require the first product to exceed the second. However, 15 is less than 16, so the correct ratio must have the first term smaller than the second.

Option C:
Option C, 5:6, is a simplified ratio that does not arise directly from 15 and 16. Reducing 15:16 would not lead to 5:6, and using 5:6 would misrepresent the slight difference between the two interest amounts.

Option D:
Option D is correct because it accurately captures the proportionality of simple interest to the product of rate and time. With equal principal, the interest amounts are in the ratio 15:16, matching the products 5 × 3 and 8 × 2 exactly.