Correct Option (D)
The problem states that 24 men and 12 women can complete a specific piece of work in 30 days. The objective is to determine the time taken by 12 men and 24 women to complete the same work.
To solve this type of problem, the individual work rates or the relative efficiency ratio between a man and a woman is a prerequisite. For instance, if one man's work output is equivalent to 'k' women's work output, this conversion factor is essential. Without this specific information, it is impossible to establish a direct equivalence or conversion between the total work potential of the initial group (24 men + 12 women) and the second group (12 men + 24 women).
Since the work efficiency ratio between a man and a woman is not provided, the overall work capacity of the second group cannot be accurately compared or calculated relative to the first group. Consequently, the data provided is inadequate to determine the number of days required.
Incorrect Options:
Options (A) "30 days", (B) "More than 30 days", and (C) "Less than 30 days or more than 30 days" cannot be concluded. As the individual efficiencies of men and women are unknown, it is not possible to ascertain whether the new group (12 men and 24 women) possesses a higher, lower, or equivalent overall work capacity compared to the original group (24 men and 12 women). Any specific numerical or comparative answer would be speculative without the necessary efficiency ratio.
