Linking simple interest and true discount: On the same sum and time, the simple interest is ₹24 while the true discount is ₹22. Find the sum due (face value) on which these were computed.

Introduction / Context: This classic TD–SI linkage uses the time-rate factor R = r * t (in decimal). For the same “sum due” S and same time, the simple interest on S is S * R, while the true discount is S * R / (1 + R). Their ratio eliminates S and gives R directly; then recover S from the given SI value.

Given Data / Assumptions:

• SI on S for time t at rate r: SI = ₹24.
• True discount on the same S, time, rate: TD = ₹22.
• Let R = r * t (in decimal units).

Concept / Approach: For the same S and R: SI = S * R and TD = S * R / (1 + R). Hence TD/SI = 1/(1 + R). Use the numerical values to find R. Then S = SI / R.

Step-by-Step Solution:

Verification / Alternative check: TD predicted = S * R / (1 + R) = 264 * (1/11) / (12/11) = 24 / 12 = ₹22, matching the given TD.

Why Other Options Are Wrong: ₹220, ₹288, ₹295, ₹242 do not satisfy both SI = 24 and TD = 22 under a single R.

Common Pitfalls: Assuming SI equals TD (that holds when SI is on present worth, not on the sum due S). Here SI is on S.

Final Answer: ₹264