Multiple choice

3 men, 4 women and 6 boys together can complete a work in 6 days. A woman does triple the work a man does and a boy does half the work a man does. How many women alone will be able to complete this work in 4 days?

  1. 9

  2. 6

  3. 8

  4. 7
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let M, W, B be the work done by a man, woman, and boy in one day. Given W=3M and B=0.5M, the group (3M+4W+6B) = (3M + 12M + 3M) = 18M. Total work = 18M * 6 days = 108M. To complete 108M in 4 days, the daily work needed is 27M. Since one woman does 3M, the number of women needed is 27M / 3M = 9.

AI explanation

Using the efficiency conversion method, let the work done by a boy in a day be 1 unit. A man does double the work of a boy, so he does 2 units, and a woman does triple the work of a man, so she does 6 units. The daily work of 3 men, 4 women, and 6 boys is 6 plus 24 plus 6, which equals 36 units, and in 6 days they complete 216 units. To finish 216 units in 4 days, the required daily work is 54 units, so dividing by 6 units per woman shows 9 women are needed.

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