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Adil and Biren together can complete a task in 20 days. Biren and Chirag together can complete the same task in 50 days. Adil and Chirag together can complete the same task in 40 days. If the same task was to be done by them alone, what would be the ratio of time taken by Adil alone to taken by Biren? A. 11 : 9 B. 11 : 3 C. 7 : 9 D. 9 : 11

Adil and Biren together can complete a task in 20 days. Biren and Chirag together can complete the same task in 50 days. Adil and Chirag together can complete the same task in 40 days. If the same task was to be done by them alone, what would be the ratio of time taken by Adil alone to taken by Biren? A. 11 : 9 B. 11 : 3 C. 7 : 9 D. 9 : 11 Correct Answer D

Let, Adil’s efficiency = x/day

Biren’s efficiency = y/day

Chirag’s efficiency = z/day

According to the question,

⇒ x + y = 1/20     … (1)

According to the question,

⇒ y + z = 1/50    …(2)

According to the question,

⇒ x + z = 1/40     …(3)

From (1) + (2) + (3) we get,

⇒ 2(x + y + z) = 1/20 + 1/50 + 1/40 = (10 + 4 + 5)/200 = 19/200

⇒ x + y + z = 19/400    … (4)

From (4) - (2) we get,

⇒ x = 19/400 - 1/50 = (19 - 8)/400

⇒ x = 11/400

From (4) - (3) we get,

⇒ y = 19/400 - 1/40

⇒ y = (19 - 10)/200

⇒ y = 9/200

∴ Ratio of efficiency of Adil and Biren = 11/400 ∶ 9/400 = 11 ∶ 9

∴ Ratio of time taken by Adil and Biren = 1/11 ∶ 1/9 = 9 ∶ 11

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