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Pipes & Cistern Questions and Answers

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41.

Two pipes P and Q can fill a tank in 10 hours and 14 hours respectively. If both pipes are opened simultaneously, how much time will be taken to fill the tank?

Answer: B

Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).

\[ \frac{1}{10} + \frac{1}{14} = \frac{7 + 5}{70} = \frac{6}{35} \]

\[ t = \frac{35}{6} = 5.8333 \text{ hours} \]

\[ 0.8333 \times 60 = 50 \text{ minutes} \]

So the tank fills in 5 hours 50 minutes.

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42.

A inlet pipe can fill a tank in 12 hours and an outlet pipe can empty the tank in 16 hours. If both the pipes are opened simultaneously, find the time taken to fill the tank.

Answer: D

As the inlet can fill the tank in 12 hours, in one hour it will fill 1/12th of the tank.
Similarly, the outlet pipe in one hour can empty 1/16th part of the tank.
If both are opened simultaneously, the part of the tank filled in one hour is:
1/12 - 1/16 = 1/48
Hence, the tank gets filled in 48 hours.

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43.

If pipe A can fill the tank in 45 minutes and pipe B in 30 minutes, find the time to fill the tank if both the pipes are opened together.

Answer: C

In 1 minute pipe A can fill 1/45th part of the tank and pipe B can fill 1/30th part of the tank. If they are opened simultaneously then in 1 minute they can fill (1/45 + 1/30) part of the tank = 1/18th part of the tank.
Hence, in 18 minutes the tank gets filled if pipes A & B are opened together.

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44.

If a pipe can fill a tank in 6 hours, find the part of tank it fills in one hour.

Answer: A

If the whole tank takes 6 hours, then in one hour the pipe fills

\[ \frac{1}{6} \text{ of the tank} \]

This reciprocal is the basic move in every pipes-and-cisterns problem: times cannot be added, but rates can.

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45.

A leak at the bottom of the tank can empty the tank in 5 hours, while an inlet pipe can fill the same tank at the rate of 6 litres per minute. When the tank is full, the inlet is opened and the tank gets empty in 8 hours due to the leakage. Find the capacity of the tank.

Answer: C

The capacity of the tank is given by C = (p*q*r)/(r - p) litres
Where, p = time in which the leakage can empty the tank in hours = 5 hours
q = rate at which the inlet fills the tank in lph = 6*60 = 360 lph
r = time in which the tank gets emptied in hours = 8 hours
Hence, C = (5*360*8)/(8 - 5)
C = 4800 litres

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46.

Pipes A and B fill a tank in 5 and 6 hours respectively. Pipe C empties the tank in 12 hours, if you open all the three pipes together this tank will be filled in?

Answer: A

It is given that Pipe A,B and C work simultaneously.

Pipe A and B are filling the tank and Pipe C is emptying it.

In 1 hour volume of tank filled by Pipe A: 1/5th

In 1 hour volume of tank filled by Pipe B: 1/6th

In 1 hour volume of tank emptied by Pipe C: 1/12th

Working together Pipe A B and C fill x volume of tank.

=>1/x = (1/5)+(1/6)-(1/12)

=>x=60/17 hours

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47.

Two pipes A and B can fill a tank in 12 and 24 minutes respectively. If both the pipes are used together, how long will it take to fill the tank?

Answer: B

Tank can be filled by pipe A in 12 minutes and pipe B in 24minutes.

=> Part filled by A in 1 minute= 1/12

=> Part filled by B in 1 minute= 1/24

=> Part filled by both in 1 minute= 1/12 + 1/24

= 3/24=1/8

Time taken to fill the entire tank = 8 minutes

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48.

Two pipes A and B can fill a cistern in 37.5 minutes and 45 minutes respectively. This cistern will be filled in half an hour if both the pipes are opened together initially and pipe B is then turned off after X minutes. What is X?

Answer: D

Let B be turned off after X minutes.

Part of water will be filled by A + B in x minutes + After tap B is closed rest filled by A in (30-x) minutes = 1

=> x/(time taken to fill the container by each separately) + 30 - x/(time taken to fill the container by A alone) = 1
=> x(2/75 + 1/45) + (30-x)2/75 = 1
=> 11x + 180 - 6x = 225

Therefore, x = 9 minutes

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49.

Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is full in 18 minutes?

Answer: C

Work in rates: a pipe that fills a tank in \( n \) units of time fills \( \tfrac{1}{n} \) of it per unit, and rates add (an emptying pipe counting negative).

A runs for the whole 18 minutes:

\[ \frac{18}{24} = \frac{3}{4} \text{ of the tank} \]

B must supply the remaining \( \tfrac{1}{4} \) at \( \tfrac{1}{32} \) per minute:

\[ t = \frac{1}{4} \times 32 = 8 \text{ minutes} \]

So B is closed after 8 minutes.

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50.

A pipe is 30 m long and is 45% longer than another pipe. Find the length of the other pipe.

Answer: A

"45% longer" means the 30 m pipe is 1.45 times the other.

\[ 30 = 1.45x \quad\Longrightarrow\quad x = \frac{30}{1.45} = 20.69 \]

Taking 45% off 30 would give 16.5, a different quantity: the percentage is measured against the shorter pipe, not the longer one.

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