The simple interest on a certain sum of money for 10 years is Rs. 1200. If the…

Concept: Simple interest is given by SI = (P × R × T) / 100, where P is the principal, R is the annual rate of interest, and T is the time in years. This equation has two independent unknowns, P and R, whenever only the interest and time are known. If a value depends on P alone (not just on the product P × R), it cannot be pinned to one number unless P is separately known — recognizing this data-insufficiency is the key idea being tested here.

Application:

1. From SI = PRT/100 with SI = 1200 and T = 10, we get P × R = (1200 × 100) / 10 = 12000.

2. If the rate becomes R + 2, the new interest is SI' = P(R+2)T/100 = PRT/100 + (P × 2 × T)/100 = 1200 + (2 × 10 × P)/100 = 1200 + 0.2P.

3. SI' depends on P alone, but only the product P × R = 12000 is fixed — P itself can take infinitely many values (with R adjusting to keep PR = 12000), so SI' cannot be pinned to a single value.

Cross-check:

1. Take P = 1200, R = 10 (so P × R = 12000): SI' = 1200 + 0.2×1200 = 1440.

2. Take P = 2400, R = 5 (so P × R = 12000 as well): SI' = 1200 + 0.2×2400 = 1680.

3. Both (P, R) pairs are equally consistent with the given data but give different new interest values (1440 vs. 1680), confirming the new interest cannot be determined.

4. As a further check: since the principal must be positive, the new interest 1200 + 0.2P is always strictly greater than Rs. 1200 — so none of 23, 78, or 65 (each well below Rs. 1200) can ever be the new interest, whatever the principal is, consistent with there being no single fixed numeric answer among the options.