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2 men and 5 women can do a piece of work in 7 days while 4 men and 4 women can do the same piece of work in 5 days. How much time will be taken by 8 men and 15 women to do the same piece of work?

2 men and 5 women can do a piece of work in 7 days while 4 men and 4 women can do the same piece of work in 5 days. How much time will be taken by 8 men and 15 women to do the same piece of work? Correct Answer 2 days

Let, a man’s efficiency = x/day

A woman’s efficiency = y/day

According to problem,

⇒ (2x + 5y) × 7 = (4x + 4y) × 5

⇒ 14x + 35y = 20x + 20y

⇒ 6x = 15y

⇒ 2x = 5y      ----(1)

Let, 8 men and 15 women can complete the work in = a days

According to problem,

⇒ (8x + 15y) ×a = (2x + 5y) × 7

⇒ (20y + 15y) × a = (5y + 5y) × 7

⇒ 35y × a = 70y

⇒ a = 2

∴ 8 men and 15 women can complete the work in 2 days

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