Twenty-four men can complete a work in sixteen days. Thirty-two women can complete the same work in twenty-four days. Sixteen men and sixteen women started working and worked for twelve days. How many more men are to be added to complete the remaining work in 2 days ?

### Concept & Target Substitution When asked to find how many *more* of a specific worker type need to be added to meet a tight deadline, solve for the total required workforce in terms of that specific worker type, and then subtract the equivalent current workforce. $$W_{remaining} = \text{Target Workforce} \times \text{Target Days}$$ ### Step-by-Step Solution * **Establish efficiency ratio:** 24 men in 16 days vs 32 women in 24 days. * Total Work = $24m \times 16 = 384m$ days. * Total Work = $32w \times 24 = 768w$ days. * Equating them: $384m = 768w \Rightarrow 1m = 2w$. * **Calculate total work:** Let's standardize on "man-days". Total work = 384 man-days. * **Determine initial work done:** The team is 16 men and 16 women. * Convert to men: $16w = 8m$. Initial team = $16m + 8m = 24m$. * They work for 12 days. Work done = $24 \times 12 = 288$ man-days. * **Calculate remaining work:** $384 - 288 = 96$ man-days. * **Determine required workforce:** The remaining 96 man-days must be finished in exactly 2 days. * Total required men for the task = $96 \text{ man-days} / 2 \text{ days} = 48 \text{ men}$. * **Find additional men needed:** Our current team is already generating the work of 24 men. * We need the work of 48 men total. * Additional men required = Total required - Current equivalent = $48 - 24 = 24$ men. ### Exam Strategy & Shortcut Recognize that the starting workforce (16m + 16w) is exactly equal to 24 men. 24 men usually take 16 days to do the *whole* job. Since they worked for 12 days, they have exactly 4 days of work left at their normal pace. To finish 4 days of work in only 2 days (half the time), you must double the workforce! Doubling 24 men means adding exactly 24 more men. No heavy arithmetic needed. ### Common Pitfall A dangerous trap is calculating that the final required team is 48 men, and then looking at the options and not realizing you have to subtract the existing equivalent workforce to find the *additional* men needed. Read the prompt carefully. ### Final Answer Therefore, the correct answer is **24**.