Question

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?

• A. 72
• B. 56
• C. 64
• D. 36

Answer 1

Answer:

B. 56

Solution: Given: 5 men and 8 women can complete a task = 34 days 4 men and 18 women can complete the same task = 28 days Formula: Total work = Efficiency × Time Calculation: Let efficiency of 1 man and 1 woman be x and y respectively, then (5x + 8y) × 34 = (4x + 18y) × 28 ⇒ (5x + 8y) × 17 = (4x + 18y) 14 ⇒ 85x + 136y = 56x + 252y ⇒ 85x - 56x = 252y - 136y ⇒ 29x = 116y ⇒ x/y = 116/29 ⇒ x : y = 4 : 1 Total work = (5 × 4 + 8 × 1) × 34 Total work = (20 + 8) × 34 Total work = 28 × 34 Efficiency of 3 men and 5 women in 1 day = (3 × 4 + 5 × 1) = 12 + 5 = 17 ∴ Time taken by 3 men and 5 women to complete the whole work = (28 × 34)/17 = 56 days