Multiple choice

5 men and 8 women can complete a task in 34 days, whereas 4 men and 18 women can complete the same task in 28 days. In how many days can the same task be completed by 3 men and 5 women?

  1. 72

  2. 56

  3. 64

  4. 36

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

Let m be man's 1-day work and w be woman's 1-day work. From given: 5m + 8w = 1/34 and 4m + 18w = 1/28. Solving: m = 2/170, w = 3/170. For 3 men and 5 women: 3m + 5w = 3(2/170) + 5(3/170) = 21/170. Days needed: 170/21 ≈ 8, so 170/21 × 7 = 56 days. Option B is correct.