Aptitude Discussion

Q. |
Pipe A fills a tank of 700 litres capacity at the rate of 40 litres a minute. Another pipe B fills the same tank at the rate of 30 litres a minute. A pipe at the bottom of the tank drains the tank at the rate of 20 litres a minute. If pipe A is kept open for a minute and then closed and pipe B is kept open for a minute and then closed and then pipe C is kept open for a minute and then closed and the cycle repeated, how long will it take for the empty tank to overflow? |

✖ A. |
42 minutes |

✖ B. |
14 minutes |

✖ C. |
39 minutes |

✔ D. |
None of these |

**Solution:**

Option(**D**) is correct

Pipe $A$ fills the tank at the rate of 40 litres a minute. Pipe $B$ at the rate of 30 litres a minute and Pipe $C$ drains the tank at the rate of 20 litres a minute.

If each of them is kept open for a minute in the order $A-B-C$, the tank will have 50 litres of water at the end of 3 minutes.

After 13 such cycles, the tank will have $13×50=650$ litres of water.

It will take $13×3=39$ minutes for the 13 cycles to be over.

At the end of the $39^{th}$ minute, Pipe $C$ will be closed and Pipe $A$ will be opened. It will add 40 litres to the tank.

Therefore, at the end of the $40^{th}$ minute, the tank will have $650+40=690$ litres of water.

At the end of the $40^{th}$ minute, Pipe $A$ will be closed and Pipe $B$ will be opened. It will add 30 litres of water in a minute.

Therefore, at the end of the $41^{th}$ minute, the tank will have $690+30=720$ litres of water.

But then at 700 litres, the tank will overflow. Therefore, Pipe $B$ need not be kept open for a full minute at the end of 40 minutes.

Pipe $B$ needs to add 10 more litres of water at the end of 40 minutes. It will take \(\left(\dfrac{1}{3}\right)^{th}\) of a minute to fill 10 litres of water.

Therefore, the total time taken for the tank to overflow

$= 40$ minutes \(+\dfrac{1}{3}\) of a minute or **40 minutes 20 seconds**.