Multiple choice

6 men can complete a piece of work in 12 days. 8 women can complete the same piece of work in 18 days whereas 18 children can complete the piece of work in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day, how many men would be required totally?

  1. 36

  2. 24

  3. 18

  4. Cannot be determined

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Calculate the work rates: 1 man = 1/72 work/day, 1 woman = 1/144 work/day, 1 child = 1/180 work/day. In 2 days, 4 men, 12 women, and 20 children complete 2 * (4/72 + 12/144 + 20/180) = 2 * (1/18 + 1/12 + 1/9) = 2 * (2/36 + 3/36 + 4/36) = 2 * (9/36) = 0.5 work. Remaining work is 0.5. To finish in 1 day, 0.5 / (1/72) = 36 men are required.

AI explanation

The total work is 72 man-days (6 men * 12 days), 144 woman-days (8 women * 18 days), and 180 child-days (18 children * 10 days), meaning 1 man equals 2 women equals 2.5 children. Converting all workers to man-equivalents, 12 women equal 6 men and 20 children equal 8 men, so the team of 4 men, 12 women and 20 children equals 18 men. In 2 days, these 18 men complete 36 man-days of work, leaving 36 man-days (72 - 36) for the final day. Finishing 36 man-days of work in 1 day requires exactly 36 men.

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