Question 41

A and B can separately do a piece of work in 20 and 15 days, respectively. They worked together for 6 days, after which B was replaced by C. If the work was finished in the next 4 days, then the number of days in which C alone could do the work will be

Solution

Work done by A in one day = $$\frac{1}{20}$$ and work done by B in one day = $$\frac{1}{15}$$

Work done by both A and B in one day = $$\frac{1}{20} + \frac{1}{15} = \frac{7}{60}$$

Work done by A and B in 6 days = $$\frac{7}{60} \times 6 = \frac{7}{10}$$

Remaining work = $$1 - \frac{7}{10} = \frac{3}{10}$$

Now, Time taken by A and B to complete the work in next 4 days is given by

$$\Rightarrow$$ (Remaining work / (A + C)'s effeciency) = Remaining time to complete the work.

$$\Rightarrow \frac{\frac{3}{10}}{\frac{1}{20} + \frac{1}{C}} = 4$$ days

$$\Rightarrow \frac{3}{10} = 4(\frac{1}{20} + \frac{1}{C})$$

$$\Rightarrow \frac{3}{10} = \frac{4}{20} + \frac{4}{C} \Rightarrow \frac{4}{C} = \frac{3}{10} - \frac{1}{5}$$

$$\Rightarrow \frac{1}{C} = \frac{1}{40}$$ (or) C = 40 days

Hence, option B is the correct answer.


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