Multiple choice

7 men and 9 women can complete a piece of work in 10 days while 5 men and 5 women can complete the same work in 15 days. Then find 10 men and 8 women to complete the same work in?

  1. 9 11/15 days

  2. 7 17/19 days

  3. 11 3/7 days

  4. 12 5/6 days

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

Let M and W be the work done by one man and one woman per day. 10(7M + 9W) = 15(5M + 5W) => 70M + 90W = 75M + 75W => 5M = 15W => M = 3W. Total work = 10(7(3W) + 9W) = 10(30W) = 300W. 10M + 8W = 10(3W) + 8W = 38W. Time = 300W / 38W = 150/19 = 7 17/19 days.

AI explanation

Let the one day work of a man be m and a woman be w. From the given data, 7m + 9w = 1/10 and 5m + 5w = 1/15, which means m + w = 1/75. Multiplying the second equation by 7 gives 7m + 7w = 7/75. Subtracting this from the first equation gives 2w = 1/150, so w = 1/300. Substituting w back gives m = 1/75 - 1/300 = 1/100. The combined one day work of 10 men and 8 women is 10/100 + 8/300 = 38/300 = 19/150. They will complete the work in 150/19 days, which is 7 17/19 days.

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