Multiple choice

$12$ men can complete a piece of work in $4$ days while $15$ women can complete the same work in $4$ days $6$ men start working on the job and after working for $2$ days all of them stopped working. How many women should be put on the job to complete the remaining work if it is to be completed in $3$ days ?

  1. $15$
  2. $18$
  3. $22$

  4. None of these
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A Correct answer
Explanation

12 men = 4 days work, so 1 man = 48 days work. 15 women = 4 days work, so 1 woman = 60 days work. 6 men work for 2 days = 6 * 2 = 12 man-days. Total work = 48 man-days. Remaining work = 48 - 12 = 36 man-days. 36 man-days = 36 * (60/48) = 45 woman-days. To finish in 3 days, women needed = 45 / 3 = 15.

AI explanation

Assume the total work is the least common multiple of the given days, which is 48 units, meaning 12 men complete 12 units daily and 15 women also complete 12 units daily. This makes the daily work of one man and one woman equal to 1 unit and 4 fifths of a unit respectively. The 6 men complete 12 units in 2 days, leaving 36 units of work, and to complete this in 3 days the required daily output is 12 units; dividing this by 4 fifths gives 15 women.

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