Multiple choice

$2$ men and $5$ women can do $\dfrac{1}{4}$th of a job in $3 $days . After $3$ days , $1 $ man joined team and they completed another$\dfrac{ 1}{4}$ th of the job in $ 2$ days . How many men can complete the job in $4$ days ?

  1. $6$
  2. $24$
  3. $34$
  4. $12$
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A Correct answer
AI explanation

Since 2 men and 5 women complete 1/4 of the work in 3 days, they complete the full work in 12 days. After 1 man joins, the new team of 3 men and 5 women completes another 1/4 of the work in 2 days, meaning they complete the full work in 8 days. Setting up the equations 12(2m + 5w) = 1 and 8(3m + 5w) = 1 gives 24m + 60w = 24m + 40w, which means 20w = 0, so women contribute nothing and 2 men complete the full work in 12 days. Therefore, to complete the job in 4 days, you need 12 / 4 = 3 times as many men, which is 6 men.

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