Multiple choice

If 2 men and 3 women can do a piece of work in 8 days and 3 men and 2 women in 7 days. In how many days can the work be done by 5 men and 4 women working together?

  1. 4 days

  2. 5 days

  3. 10 days

  4. 15 days

  5. None of these

Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let 1 day's work for 1 man = m and 1 woman = w. From given: 2m + 3w = 1/8 and 3m + 2w = 1/7. Solving: multiply first by 3: 6m + 9w = 3/8. Multiply second by 2: 6m + 4w = 2/7. Subtract: 5w = 3/8 - 2/7 = (21-16)/56 = 5/56, so w = 1/56. Then m = 1/1568. For 5M + 4W: 5(1/1568) + 4(1/56) = 5/1568 + 4/56 = 5/1568 + 112/1568 = 117/1568 = 1/4. Therefore, work completes in 4 days.