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A and B can complete a task in 80 days, B and C can complete it in 60 days while C and A can complete the same task together in 48 days. How many days will A, B, and C together take to complete the task?

A and B can complete a task in 80 days, B and C can complete it in 60 days while C and A can complete the same task together in 48 days. How many days will A, B, and C together take to complete the task? Correct Answer 40

(A + B) can complete a task in 80 days

⇒ (A + B)’s 1 day’s work = 1/80

Now, (B + C) can complete a task in 60 days

⇒ (B + C)’s 1 day’s work = 1/60

As, (C + A) can complete a task in 48 days

⇒ (C + A)’s 1 day’s work = 1/48

According to problem,

⇒ 2(A + B + C) = (1/80) + (1/60) + (1/48)

⇒ 2(A + B + C) = 1/20

⇒ A + B + C = 1/40

∴ (A + B + C) together can complete the task in 40 days

Alternate Solution:

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Efficiency of (A + B + C) when they work together = (1/2){Efficiency of (A + B) + Efficiency of (B + C) + Efficiency of (A + C)}

= (3 + 4 + 5)/2 = 6

Time taken by (A + B + C) to complete the work when they work together = 240/6 = 40 days

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