# CAT Practice : Pipes cisterns, Work time

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Classic Work - Time Question!!

## Typing Pages

Q.22: A certain number of pages need to be typed. A, B and C are assigned to do this job. However, C leaves after 4 days when 40% of the job was complete. In this way, it takes 13 days to finish the job. Also, B can type twice as fast as A. How much would the fastest worker take to type the entire set of pages alone?
1. 22.5 days
2. 45 days
3. 30 days
4. 20 days

Choice A. 22.5 days

## Detailed Solution

A and B take 9 days to complete the remaining 60% of the job.

Therefore, in one day A and B can complete – $\frac{60}{9} = \frac{20}{3}%$ of the job

Since B is twice as fast as A,

B can finish = $\frac{20}{3} * \frac{2}{3} = \frac{40}{9}%$ of the job in a day

A can finish= $\frac{20}{3} * \frac{1}{3} = \frac{20}{9}%$ of the job in a day

In the first 4 days. A and B would have finished = $\frac{20}{3} * 4 = \frac{80}{3} %$ of the job

Therefore, C would have finished = $40 % - \frac{80}{3}% = \frac{40}{3}%$ of the job in 4 days

So, in a day C finishes = $\frac{40}{12}%$ of the job

Thus, clearly B is the fastest among the three workers

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## More questions from Pipes Cisterns, Work Time

Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.