Partnership profit share with time weights – UGC NET Question

In partnership problems, the profit is divided in the ratio of capital multiplied by time. Taking capitals as 3k, 5k and 7k for A, B and C and times as 2, 4 and 6 years, their effective investments are 3k × 2 = 6k, 5k × 4 = 20k and 7k × 6 = 42k. The ratio 6:20:42 simplifies to 3:10:21. The sum of these parts is 34, so B’s share is (10/34) of ₹1,36,000, which equals ₹40,000.

Option A:
Option A is correct because the calculation (10/34) × 1,36,000 gives exactly ₹40,000, and using 3/34 and 21/34 for A and C yields the remaining profit. The three shares add up neatly to ₹1,36,000, confirming that the ratio of effective investments has been applied correctly. Hence, ₹40,000 accurately represents B’s entitlement.

Option B:
Option B, ₹38,000, would not correspond to the fraction 10/34 of the total profit. If we assign ₹38,000 to B, the remaining amount for A and C would not then be divisible in the ratio 3:21 without leaving a remainder or altering the initial capital-time structure. Therefore, ₹38,000 is inconsistent with the proportional rule.

Option C:
Option C, ₹48,000, would represent a larger share than warranted by the 10 parts out of 34. Using ₹48,000 for B implies that B’s effective contribution outweighs that of C more than the 10:21 ratio allows. This contradicts the original investment-time data, so ₹48,000 cannot be correct.

Option D:
Option D, ₹52,000, is even higher and would require B’s share to be close to or greater than C’s share, which is not supported by the ratio 3:10:21. The necessary rebalancing of the remaining profit would distort the intended proportions. As a result, ₹52,000 does not match the proportional distribution.