Aptitude Discussion

Q. |
There are 12 pipes that are connected to a tank. Some of them are fill pipes and the others are drain pipes. Each of the fill pipes can fill the tank in 8 hours and each of the drain pipes can drain the tank completely in 6 hours. If all the fill pipes and drain pipes are kept open, an empty tank gets filled in 24 hours. How many of the 12 pipes are fill pipes? |

✖ A. |
6 |

✖ B. |
8 |

✔ C. |
7 |

✖ D. |
5 |

**Solution:**

Option(**C**) is correct

Let there be '$n$' fill pipes attached to the tank.

Therefore, there will be $12–n$ drain pipes attached to the tank

Each fill pipe fills the tank in 8 hours.

Therefore, each of the fill pipes will \(\left(\dfrac{1}{8}\right)^{th}\)of the tank in an hour.

Hence, $n$ fill pipes will fill \(n\times \dfrac{1}{8}=\dfrac{n}{8}\)of the tank in an hour.

Each drain pipe will drain the tank in 6 hours.

Therefore, each of the drain pipes will drain \(\left(\dfrac{1}{6}\right)^{th}\)of the tank in an hour.

Hence, $(12−n)$ drain pipes will drain

\((12-n)\times \dfrac{1}{6}=\dfrac{12-n}{6}\)of the tank in an hour.

When all these 12 pipes are kept open, it takes 24 hours for an empty tank to overflow.

Therefore, in an hour \(\left(\dfrac{1}{24}\right)^{th}\) of the tank gets filled.

Hence,

\(\dfrac{n}{8}-\dfrac{12-n}{6}=\dfrac{1}{24}\)

\(\dfrac{3n-4(12-n)}{24}=\dfrac{1}{24}\)

$⇒ 7n−48=1$

$⇒ 7n=49$ or $n=\textbf{7}$

**Edit:** For an alternative solution, check comment by **PULOK KHAN.**

**Vaibhav**

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**PULOK KHAN**

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Let there are fill pipes $=n$

so, drain pipes $= 12-n$

Hence,

$8n-6(12-n)=24$

$14n=96$

$n=7$

LCM method:

Let LCM of two pipes be 24 (6,8)

Work done per hour by fill pipe be 3 unit/hour

Work done per hour by drain pipe be 4 unit/hour

Now as you can see, the efficiency of the drain pipe is more than that of the fill pipe, so the number of fill pipe has been more than drain pipe. This will eliminate the two choices in the option i.e 5,6.

Now, we can check the other two choices.

if we have 8 fill pipes

3 * 8 - 4* 4=> 24-16 => 8 unit per hour. This will fill the tank in 3 hours but we have to fill the tank in 24 hours.

consider 7 fill pipes

3 * 7 - 4 * 5 => 21 - 20 = 1 unit per. This will fill the tank in 24 hours.

Hence, option C is the answer.