# CAT Practice : Pipes cisterns, Work time

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Finding one answer is usually far easier than finding "boundary conditions". But this boundary condition thing can be very instructive.

## Work Time

Q.4: 4 men and 6 women complete a task in 24 days. If the women are at least half as efficient as the men, but not more efficient than the men, what is the range of the number of days for 6 women and 2 men to complete the same task?
1. 30 to 33.6 days
2. 32 to 35 days
3. 33.6 to 35 days
4. 30 to 35 days

Choice A. 30 to 33.6 days

## Detailed Solution

4m and 6w finish in 24 days.
In one day, 4m + 6w = ${1 \over 24}$ of task.

In these questions, just substitute extreme values to get the whole range
If a woman is half as efficient as man
4m + 3m = ${1 \over 24}$, 7m = ${1 \over 24}$, m = ${1 \over 168}$
6w + 2m = 3m + 2m = 5m, 5m will take ${168 \over 5}$ days = 33.6 days

If a woman is as efficient as a man
4m + 6w finish in 24 days
10m finish ${1 \over 24}$ of task in a day
6w + 2m = 8m, 8m will take ${240 \over 8}$ = 30 days to finish the task.

So, the range = 30 to 33.6 days. The new team will take 30 to 33.6 days to finish the task. Choice (A)

Correct Answer: 30 to 33.6 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.