# CAT Practice : Pipes cisterns, Work time

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If they work together, will the number of days taken decrease?

## Pipes Cisterns - Work Time

Q.13: A can complete a task in 12 days. B can complete the task in 18 days. If A and B work on this same task in alternate days starting with A, in how many days do they finish the entire task?
1. 10.8 days
2. 14.33 days
3. 11 days
4. 8.4 days

Choice B. 14.33 days

## Detailed Solution

A can complete a task in 12 days and B can complete the task in 18 days. So,
In one day, A can do $\frac{1}{12}$, in one day B can do $\frac{1}{18}$.
In two days, they can complete $\frac{1}{12}$ + $\frac{1}{18}$ = which is $\frac{5}{36}$.
In 4 days, they can finish $\frac{10}{36}$, and so on.
We can have 7 such sets of 2days each.
So, at the end of 14 days, they would have done $\frac{35}{36}$ of task.
On the 15th day A would begin work with $\frac{1}{36}$of the task to finish. He can finish $\frac{1}{12}$ in a day. So, he would take one-third of a day. So, they can finish the whole task in 14.33 days.

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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.