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A and B together can complete a task in 40 days. B and C together can complete the same task in 50 days. A and C together can complete the same task in 60 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone?

A and B together can complete a task in 40 days. B and C together can complete the same task in 50 days. A and C together can complete the same task in 60 days. What is the respective ratio of the number of days taken by A when completing the same task alone to the number of days taken by C when completing the same task alone? Correct Answer 7 : 13

A and B can complete a task in 40 days

⇒ (A + B)’s 1 day’s work = 1/40 unit

B and C can complete a task in = 50 days

⇒ (B + C)’s 1 day’s work 1/50 unit

C and A can complete a task in = 60 days

⇒ (C + A)’s 1 day’s work 1/60 unit

(A + B + C)’s 1 day’s work = 1/2 × (1/40 + 1/50 + 1/60)

⇒ 1/2 × (15 + 12 + 10)/600

⇒ 37/1200 unit

A’s 1 day’s work = 37/1200 – 1/50 = 13/1200 unit

⇒ A can complete the work in = 1200/13 days

C’s 1 day’s work = 37/1200 – 1/40 = 7/1200

⇒ C can complete the work in = 1200/7 days

∴ Required ratio = 1200/13 ∶ 1200/7 = 7 ∶ 13

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