Multiple choice

A piece of work can be completed in 2 days by 4 men. 4 women can complete the same piece of work in 4 days, whereas, 5 children can complete the same piece of work in 4 days. If 2 men, 4 women and 10 children work together, in how many days can the work be completed?

  1. 1 day

  2. 3 days

  3. 2 days

  4. 4 days

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

Work = 4 men * 2 days = 8 man-days. 4 women * 4 days = 16 woman-days. 5 children * 4 days = 20 child-days. 1 man = 1/8 work/day, 1 woman = 1/16 work/day, 1 child = 1/20 work/day. 2 men + 4 women + 10 children = 2/8 + 4/16 + 10/20 = 1/4 + 1/4 + 1/2 = 1 work/day. Time = 1/1 = 1 day.

AI explanation

Calculate the total work by finding the least common multiple of the days taken by the different groups, which is 16 units. One man does 2 units a day, one woman does 1 unit a day, and one child does 0.8 units a day. Working together, 2 men, 4 women, and 10 children complete 4 plus 4 plus 8 units daily, totaling 16 units per day. Since the group completes 16 units in a single day, the total time taken is 1 day.

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