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A and B can do a work alone in 12 days and 8 days respectively. They undertook to do a work together, but B left the work after 2 days. Then, the remaining work was completed by A together with C in 3 days. If C got Rs. 600 as his share, for how much money did they undertook to do the work?

A and B can do a work alone in 12 days and 8 days respectively. They undertook to do a work together, but B left the work after 2 days. Then, the remaining work was completed by A together with C in 3 days. If C got Rs. 600 as his share, for how much money did they undertook to do the work? Correct Answer Rs. 1800

A’s 1 day work = 1/12

∵ A worked for 2 + 3 = 5 days,

⇒ Share of work done by A = 5 × 1/12 = 5/12

Similarly,

B’s 1 day work = 1/8

But, B worked for only 2 days,

⇒ Share of work done by B = 2 × 1/8 = 1/4

⇒ Share of work done by C = 1 – (5/12 + 1/4) = 1 – 2/3 = 1/3

Now,

Ratio of wages = Ratio of work done = 5/12 ∶ 1/4 ∶ 1/3 = 5 ∶ 3 ∶ 4

Sum of ratios = 5 + 3 + 4 = 12

⇒ C’s wages = 4/12 × Total amount = 600

⇒ Total amount = 3 × 600 = Rs. 1800

∴ They undertook to do the work for Rs. 1800

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