Multiple choice

A boy alone, a girl alone and a woman alone can complete a piece of work in 30 days, 60 days and 80 days, respectively. How many women must assist 4 boys and 6 girls so as to complete the work in 3 days?

  1. 6

  2. 8

  3. 9

  4. 21

  5. 29
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Work rates: Boy=1/30, Girl=1/60, Woman=1/80. Total work needed in 3 days = 1. Work done by 4 boys and 6 girls in 3 days = 3 * (4/30 + 6/60) = 3 * (2/15 + 1/10) = 3 * (4/30 + 3/30) = 3 * (7/30) = 21/30 = 7/10. Remaining work = 3/10. Let w be number of women: w * (1/80) * 3 = 3/10. w/80 = 1/10, w = 8.

AI explanation

Assume the total work is the least common multiple of 30, 60, and 80, which is 240 units. The one-day work of a boy is 8 units, a girl is 4 units, and a woman is 3 units. The combined one-day work of 4 boys and 6 girls is 32 + 24 = 56 units. To finish the 240 units in 3 days, the daily required output is 80 units. The women must provide the remaining 80 minus 56 = 24 units of work per day, so the required number of women is 24 divided by 3, which equals 8 women.

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