UGC NET Questions (Paper – 1)

Statements A, C and D express standard partnership principles. A is correct because profit shares are proportional to capital multiplied by duration of investment. C correctly defines a sleeping partner’s role. D is true as reducing capital during the year reduces the effective capital–time product. B is false since equal capital and time lead to a 1:1 ratio, and E is false because time is crucial when investments are made for different periods. Hence, A, C and D only are correct.

Option A:
Option A is correct because it combines the basic rule of capital–time proportionality with the concept of sleeping partners and the effect of withdrawing capital, while excluding B and E, which misstate profit ratios and the role of time.

Option B:
Option B is incorrect because it includes B, which incorrectly fixes the profit share at 1:2 even when capital and time are equal, thus contradicting the proportional rule.

Option C:
Option C is wrong as it also includes E, wrongly claiming that time is irrelevant in partnership problems, and therefore mixes incorrect statements with correct ones.

Option D:
Option D is incomplete since it omits A and includes only C and D, failing to explicitly state the capital–time proportionality on which partnership questions are based.

In partnership problems, profit is divided in the ratio of “capital × time”. Taking capitals 5k, 7k and 9k for A, B and C, and times 12, 10 and 8 months, their effective investments are 5k × 12 = 60k, 7k × 10 = 70k and 9k × 8 = 72k. These are in the ratio 60:70:72. The sum of the ratio parts is 202, so C’s share is (72/202) of ₹2,02,000, which equals ₹72,000.

Option A:
Option A, ₹60,000, corresponds to 60 parts out of 202 and would be A’s share if we followed the correct method. Assigning this to C would contradict both the given investment ratio and the time periods. It undervalues C’s contribution, which is actually the largest.

Option B:
Option B is correct because it matches the 72 parts assigned to C in the 60:70:72 ratio. Multiplying the total profit by 72/202 leads exactly to ₹72,000, and the remaining profits allocate correctly to A and B when their parts are used. This ensures the distribution honours both capital and time contributions.

Option C:
Option C, ₹84,000, would represent a different fraction of the total profit and would imply that C’s effective investment is larger than 72 parts out of 202. That would disturb the precise ratio derived from 5:7:9 and the corresponding time periods. Hence ₹84,000 does not reflect the correct proportional sharing.

Option D:
Option D, ₹90,000, exceeds even Option C and would require a much stronger claim for C’s investment than is supported by the data. If we tried to back-calculate the implied ratio, the figures would no longer match the product of capital and time given in the question. Thus, ₹90,000 cannot be C’s correct share.