Multiple choice

30 men can finish a piece of work in 10 days, whereas it takes 12 women to finish it in 10 days. If 15 men and 6 women undertake to complete the same work, how many days will they take to complete the work?

  1. 20

  2. 15

  3. 12

  4. 10

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

30 men = 10 days, so 1 man = 300 man-days. 12 women = 10 days, so 1 woman = 120 woman-days. 15 men = 15/300 = 1/20 of work per day. 6 women = 6/120 = 1/20 of work per day. Combined rate = 1/20 + 1/20 = 2/20 = 1/10. Time = 10 days.

AI explanation

Using the work equivalence method, 30 men working for 10 days equals 300 man-days, and 12 women working for 10 days equals 120 woman-days. This means 300 man-days equals 120 woman-days, so 5 men equal 2 women. Therefore, 15 men equal 6 women, meaning a team of 15 men and 6 women is effectively two teams of 6 women each. Since 12 women finish the work in 10 days, this combined team will also finish it in 10 days.

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