A, B and C together can complete a certain work in 37 days. B and C together can complete the same work in 74 days. B is 50% more efficient than A. A, B and C work together for 28 days. B alone will complete the remaining work in:
12 days
Let total work be the LCM of 37 and 74, i.e. 74 units, so rates come out in whole units.
One day's work of (A + B + C) \(= \frac{74}{37} = 2\) units, and one day's work of (B + C) \(= \frac{74}{74} = 1\) unit.
Therefore, A's one day's work \(= (A+B+C) - (B+C) = 2 - 1 = 1\) unit per day.
B is 50% more efficient than A, so B's one day's work \(= 1.5 \times 1 = 1.5\) units per day.
In 28 days, A, B and C together do \(28 \times 2 = 56\) units. Remaining work \(= 74 - 56 = 18\) units.
Time for B alone to finish 18 units \(= \frac{18}{1.5} = 12\) days.
Hence, B alone will complete the remaining work in 12 days.
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