Aptitude Discussion

Q. |
There are 12 pipes attached to a tank. Some of them are fill pipes and some are drain pipes. Each of the fill pipes can fill the tank in 12 hours, while each of the drain pipes will take 24 hours to drain a full tank completely. If all the pipes are kept open when the tank was empty, it takes 2 hours for the tank to overflow. How many of these pipes are drain pipes? |

✖ A. |
6 |

✖ B. |
11 |

✔ C. |
4 |

✖ D. |
7 |

**Solution:**

Option(**C**) is correct

There are 12 pipes attached to the tank. Let $n$ of them be fill pipes. Therefore, there will be $12−n$ drain pipes.

Each fill pipe, fills the tank in 12 hours. Therefore, \(\left(\dfrac{1}{12}\right)^{th}\) of the tank gets filled every hour by one fill pipe.

$n$’ fill pipes will, therefore, fill \(\left(\dfrac{n}{12}\right)^{th}\)of the tank in an hour.

Each drain pipe drains the tank in 24 hours. That is, \(\left(\dfrac{1}{24}\right)^{th}\)of the tank gets drained by one drain pipe every hour.

$12−n$ drain pipes, will therefore, drain \(\dfrac{12-n}{24}\) of the tank in an hour.

When all the pipes are open when the tank is empty, it takes 2 hours for the tank to overflow. i.e. \(\dfrac{1}{2}\) the tank gets filled every hour.

Equating the information, we get \(\dfrac{n}{12}-\dfrac{12-n}{24}=\dfrac{1}{2}\)

\(\dfrac{2n+n-12}{24}=\dfrac{1}{2}\)

$3n−12=12$ or $3n=24$ or $n=8$.

Therefore, there are 8 fill pipes and (12−8)= **4 drain pipes.**

**Atharva Joshi**

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**Krishnakumar**

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*

Time to fill = 12hrs

Time to drain = 24hrs

so ratio of time = 12:24=1:2

time is inversely proportional to no of pipes

hence

drain pipes = x

fill pipes = 2x

total pipes = 12

x+2x=12

3x=12

x=4-> drain pipes

**Vaibhav Gupta**

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*

Let fill pipes are x

And drain pipes are y

So, x+y=12..............…..........(1)

Also,x/12-y/24=1/2.............(2)

Solving them we get y=4

Thus no. Of drain pipes are 4.

Or we can logically think that the time ratio is 1:2 so keeping that in mind that water overflows in 2 hrs the number of drain pipes should be less than no of filling pipes so the only available option was 4