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A and B together can complete a work in 40 days. They started together but after 8 days A left the work. The remaining work is completed by B alone in 48 more days. In how many days can A complete the entire work alone?

A and B together can complete a work in 40 days. They started together but after 8 days A left the work. The remaining work is completed by B alone in 48 more days. In how many days can A complete the entire work alone? Correct Answer 120

(A + B) can complete a work in = 40 days

∴ (A + B)’s 1 day’s work = 1/40      ----(1)

∴ (A + B)’s 8 day’s work = 8/40 = 1/5

∴ Remaining work = 1 - 1/5 = 4/5

∴ B completes 4/5 work in = 48 days

∴ B can complete the work in = 48 × 5/4 = 60 days

∴ B’s 1 day’s work = 1/60      ----(2)

From (1) and (2) we get,

A’s 1 day’s work,

⇒ 1/40 - 1/60

⇒ (3 - 2)/120

⇒ 1/120

∴ A can complete the work in = 120 days

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