Multiple choice

A team of 16 women and 6 men can complete a baking assignment in 20 days, while another team with 20 women and 16 men can do the same assignment in 12 days. Calculate the time taken by 15 women and 15 men to do the same assignment.

  1. 10 days

  2. 14.32 days

  3. 15.45 days

  4. 20 days

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

Let W be work of a woman, M be work of a man. 20(16W + 6M) = 12(20W + 16M). 320W + 120M = 240W + 192M. 80W = 72M => 10W = 9M. Total work = 20(16W + 6(10/9)W) = 20(16W + 6.66W) = 453.33W. New team = 15W + 15M = 15W + 15(10/9)W = 15W + 16.66W = 31.66W. Days = 453.33 / 31.66 = 14.32.

AI explanation

Let one woman and one man do w and m work in a day. From the given teams, 16w plus 6m equals 1/20 and 20w plus 16m equals 1/12. Solving these equations gives w equals 1/1200 and m equals 1/600. The one day work of 15 women and 15 men is 15/1200 plus 15/600, which equals 45/1200 or 3/80. The time taken by them to do the assignment is 80 divided by 3, which is approximately 14.32 days.

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