Ratio of daily work from time taken – UGC NET Question

If A alone finishes the work in 10 days, A’s one-day work is 1/10 of the job. If B alone finishes in 15 days, B’s one-day work is 1/15. The ratio of work done by A to work done by B in one day is (1/10):(1/15) = 15:10, which simplifies to 3:2. Thus, the required ratio is 3:2.

Option A:
Option A, 2:3, reverses the correct comparison and implies B does more work per day than A, suggesting B is faster. This contradicts the completion times, because A finishes in fewer days than B and must therefore have the higher daily rate.

Option B:
Option B, 4:3, does not match the exact fraction (1/10)/(1/15) = 15/10 = 3/2. While 4:3 is close numerically to 3:2, the calculation from the given times unambiguously leads to 3:2, not 4:3. Hence 4:3 is incorrect.

Option C:
Option C is correct because it faithfully reflects the inverse relationship between time and rate for a fixed amount of work. Shorter time (10 days) corresponds to a larger rate, and the ratio of these rates simplifies precisely to 3:2.

Option D:
Option D, 5:3, exaggerates the difference between the two rates beyond what is implied by 10 and 15 days. Using 5:3 would not produce the correct individual times if we converted back from the rate ratio, so it cannot be accepted.