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5 men and 6 boys can do a work in 6 days and 4 women and 1 boy can do the same work in 14 days. If 3 men and 5 boys can do the same work in 9 days, than, how many days can 2 men and 3 boys do the same work?

5 men and 6 boys can do a work in 6 days and 4 women and 1 boy can do the same work in 14 days. If 3 men and 5 boys can do the same work in 9 days, than, how many days can 2 men and 3 boys do the same work? Correct Answer 14 days

(5M + 6B) × 6 = (4W + 1B) × 14

⇒ 30M + 36B = 56W + 14B

⇒ 30M + 22B = 56W       ----(1)

(4W + 1B) × 14 = (3M + 5B) × 9

⇒ 56W + 14B = 27M + 45B

⇒ 56W = 27M + 31B      ----(2)

From (1) and (2)

⇒ 30M + 22B = 27M + 31B

⇒ 3M = 9B

⇒ M = 3B

⇒ M : B = 3 : 1      ----(3)

From(2)

⇒ 56W = 27 × 3B + 31B = 112B

⇒ W = 2B

⇒ W : B = 2 : 1     ----(4)

From (3) and (4)

Respective ratio of efficiency, M : W : B = 3 : 2 : 1

⇒ Total work = (5M + 6B) × 6 = (15 + 6) × 6 = 21 × 6 = 126

∴ Time taken by 2 men and 3 boys = 126/(2 × 3 + 3 × 1) = 126/9 = 14 days

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