24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?

(a) 30 days
(b) More than 30 days
(c) Less than 30 days or more than 30 days
(d) Data is inadequate to draw any conclusion ✓ UPSC's answer

Why the answer is (d)

• The problem provides the combined work rate of 24 men and 12 women but does not specify the individual work rates of a man and a woman.

• Without knowing the ratio of efficiency between a man and a woman, the total work capacity of the new group (12 men and 24 women) cannot be determined relative to the original group.

• If men are more efficient than women, the new group might take more than 30 days; if women are more efficient, it might take less.

• Since the relative efficiency is unknown, the number of days required cannot be calculated or compared to 30 days.

• Therefore, the data provided is inadequate to draw any conclusion.

Why the other options are wrong

(a) 30 days: This option assumes that men and women have equal efficiency, which is not stated in the problem.
(b) More than 30 days: This option assumes that men are significantly more efficient than women, which is not supported by the given data.
(c) Less than 30 days or more than 30 days: This option suggests the answer depends on unknown variables, but the correct classification for such a scenario in this context is that the data is inadequate to draw a specific conclusion.

Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2022, held on 5 June 2022. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.