Question 42

B can do a piece of work in 6 hours, B and C together can do it in 4 hours, and A, B and C together in $$2\frac{2}{3}$$ hours. In how many hours can A and B together do the same piece of work?

Solution

Work done by B in one hour = $$\frac{1}{6}$$

Work done by B and C together in one hour = $$\frac{1}{B} + \frac{1}{C} = \frac{1}{6} + \frac{1}{12} = \frac{1}{12}$$

Work done by A, B and C together in one hour,

$$\frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{3}{8}$$

$$\frac{1}{A} + \frac{1}{6} + \frac{1}{12} = \frac{3}{8}$$

$$\frac{1}{A} = \frac{3}{8} - \frac{1}{6} - \frac{1}{12}$$

$$\frac{1}{A} = \frac{9 - 4 - 2}{24} = \frac{1}{8}$$

Work done by A and B together in one hour = $$\frac{1}{A} + \frac{1}{B} = \frac{1}{8} + \frac{1}{6} = \frac{7}{24}$$

Total work done by A and B together = $$\frac{24}{7}$$ (or) $$3\frac{3}{7}$$ hours

Hence, option D is the correct answer.

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