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A, B and C were paid Rs. 8000 for a piece of work which they finished together. Find the shares of A. Statement I: All three together can finish the work in 7.5 days while C alone takes 20 days to complete the work. Statement II: A and B together can finish the work in 12 days.

A, B and C were paid Rs. 8000 for a piece of work which they finished together. Find the shares of A. Statement I: All three together can finish the work in 7.5 days while C alone takes 20 days to complete the work. Statement II: A and B together can finish the work in 12 days. Correct Answer Both Statements I and II together are not sufficient to answer the question.

We need to get the efficiencies of A, B and C or the units of work done by them individually.

Statement I:

All three together can finish the work in 7.5 days while C alone takes 20 days to complete the work.

Suppose total work is 60 units (LCM of 7.5 and 20)

⇒ Efficiency of C = 60/20 = 3

⇒ Efficiency of (A + B + C) = 60/7.5 = 8

⇒ Efficiency of (A + B) = 8 – 3 = 5

Efficiency of A can’t be determined.

Combining statement II:

A and B together can finish the work in 12 days.

Efficiency of (A + B) = 60/12 = 5

Efficiency of A can’t be determined.

∴ Both Statements I and II together are not sufficient to answer the question.

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