Multiple choice

5 men can complete a work in 12 days, 8 women can complete it in 18 days and 10 children can complete the same work in 24 days. In how many days can 10 men, 12 women and 8 children complete the same work?

  1. 3 9/17 days

  2. 4 2/9 days

  3. 5 3/7 days

  4. 6 6/11 days

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

Calculate the work rate: 1 man = 1/60 work/day, 1 woman = 1/144 work/day, 1 child = 1/240 work/day. 10 men + 12 women + 8 children = 10/60 + 12/144 + 8/240 = 1/6 + 1/12 + 1/30 = (10+5+2)/60 = 17/60. Time = 60/17 = 3 9/17 days.

AI explanation

Using the LCM method, let the total work be 360 units. The daily work done by 5 men is 30 units, by 8 women is 20 units, and by 10 children is 15 units, meaning 1 man does 6 units, 1 woman does 2.5 units, and 1 child does 1.5 units per day. The combined daily work of 10 men, 12 women, and 8 children is (60 + 30 + 12) = 102 units. Dividing the total work of 360 units by 102 units per day gives the completion time of 3 9/17 days.

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