Multiple choice

$24$ men can complete a work in $16$ days, $32$ women can complete the same work in $24$ days. $16$ men and $16$ women started working and worked for $12$ days. How many more men are to be added to complete the remaining work in $2$ days?

  1. $16$
  2. $24$
  3. $36$
  4. $48$
Reveal answer Fill a bubble to check yourself
B Correct answer
AI explanation

The total work is the least common multiple of 16 and 24, which is 48 units, meaning 24 men have a daily rate of 3 units and 32 women have a daily rate of 2 units. This makes the daily work of one man equal to 1 by 8 and one woman equal to 1 by 16, so 16 men and 16 women complete 3 units daily, doing 36 units in 12 days. The remaining 12 units must be completed in 2 days by 16 men plus some extra men and 16 women, requiring a daily total of 6 units; since 16 women provide 1 unit, the men must provide 5 units, which requires 40 men total, meaning 24 more men are added.

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