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A and B alone can do a work in 8 days and 12 days respectively. They together do a work for Rs. 1200 but A left the work in between and B completed the remaining work alone. If A received Rs. 120 less than his actual share then, for how many days did B worked alone to complete the work?

A and B alone can do a work in 8 days and 12 days respectively. They together do a work for Rs. 1200 but A left the work in between and B completed the remaining work alone. If A received Rs. 120 less than his actual share then, for how many days did B worked alone to complete the work? Correct Answer 2 days

⇒ A’s 1 day work = 1/8

⇒ B’s 1 day work = 1/12

Now,

⇒ Ratio of their shares = Ratio of their work efficiencies = (1/8) ∶ (1/12) = 12 ∶ 8 = 3 ∶ 2

⇒ A’s actual share = (3/5) × 1200 = Rs. 720

As, A left the work in between so A received Rs. 120 less than his actual share

⇒ A’s share = 720 - 120 = Rs. 600

⇒ B’s share = 1200 - 600 = Rs. 600

⇒ Ratio of their work done = Ratio of their shares = 600 ∶ 600 = 1 ∶ 1

Now,

⇒ Work done by A = Work done by B = 1/2

⇒ No. of days for which A worked = (1/2)/(1/8) = 4 days

⇒ No. of days for which B worked = (1/2)/(1/12) = 6 days

∴ B worked alone for = 6 - 4 = 2 days

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