Class 8 Pipes and Cisterns — practice questions with answers

Direct and Inverse Proportions · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.

1. A pipe can fill a tank in 12 hours. Another pipe can empty it in 18 hours. If both are opened, how long will it take to fill the tank?

A7 1/5 hours
B6 hours
C30 hours
D36 hours

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Answer: D) 36 hours

Net rate

= \frac{1}{12} - \frac{1}{18} = \frac{3 - 2}{36} = \frac{1}{36}

of the tank per hour, so 36 hours. 7 1/5 h wrongly adds the two rates.

2. Pipe A fills a tank in 3 hours; pipe B empties it in 5 hours. A is opened, and B is opened 1 hour later. How long after A was opened is the tank full?

A6 hours
B7 1/2 hours
C5 hours
D4 1/2 hours

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Answer: A) 6 hours

After 1 h:

\frac{1}{3}

. Left

\frac{2}{3}

at net

\frac{1}{3} - \frac{1}{5} = \frac{2}{15}

: 5 hours. Total 6 hours.

3. Pipe A fills a tank in 16 minutes and pipe B in 24 minutes. They are opened alternately for 1 minute each, starting with A. How long does the tank take to fill?

A19 minutes
B19 1/3 minutes
C20 minutes
D18 minutes

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Answer: A) 19 minutes

Each 2-minute cycle fills

\frac{1}{16} + \frac{1}{24} = \frac{5}{48}

. After 9 cycles (18 min):

\frac{45}{48}

. Minute 19 is A's turn and adds

\frac{3}{48}

, exactly the rest: 19 minutes.

4. Two pipes together fill a tank in 12 hours. If one of them alone takes 20 hours, how long does the other take alone?

A30 hours
B8 hours
C32 hours
D16 hours

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Answer: A) 30 hours

\frac{1}{12} - \frac{1}{20} = \frac{5 - 3}{60} = \frac{1}{30}

: 30 hours.

5. Pipe A fills a tank in 3 hours and pipe B fills it in 6 hours. How long do they take together?

A4 1/2 hours
B2 hours
C9 hours
D3 hours

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Answer: B) 2 hours

\frac{1}{3} + \frac{1}{6} = \frac{1}{2}

: 2 hours.

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