Class 8 Leaks and Changing Pipes — 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 tank of 960 litres is filled by a pipe in 8 hours. What is the pipe's flow in litres per hour?

A120 litres
B96 litres
C80 litres
D160 litres

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Answer: A) 120 litres

960 \div 8 = 120

litres an hour.

2. Pipe A fills a pool in 10 hours and pipe B in 15 hours. A is opened at 8 a.m. and B at 9 a.m. When is the pool full?

A2 p.m.
B3 p.m.
C1:30 p.m.
D2:24 p.m.

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Answer: D) 2:24 p.m.

By 9 a.m.:

\frac{1}{10}

. Left

\frac{9}{10}

\frac{1}{6}

: 5.4 h = 5 h 24 min after 9 a.m., which is 2:24 p.m.

3. A pipe fills a cistern in 15 minutes. After 5 minutes a leak starts, and the cistern is full 15 minutes after that. How long would the leak take to empty the full cistern?

A30 minutes
B45 minutes
C15 minutes
D60 minutes

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Answer: B) 45 minutes

After 5 min:

\frac{1}{3}

. The other

\frac{2}{3}

took 15 min: net

\frac{2}{45}

. Leak

= \frac{3}{45} - \frac{2}{45} = \frac{1}{45}

: 45 minutes.

4. A tank has an inlet (fills in 6 h) and an outlet (empties in 8 h). They are opened alternately for 1 hour each, starting with the inlet. After 4 hours, what fraction of the tank is full?

A1/12
B1/24
C1/6
D7/24

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Answer: A) 1/12

Each 2-hour cycle:

\frac{1}{6} - \frac{1}{8} = \frac{1}{24}

. Two cycles:

\frac{2}{24} = \frac{1}{12}

5. A school's overhead tank is filled by a motor in 40 minutes. The taps below drain it in 1 hour when all are open. If the motor is started while all the taps are running, how long does the tank take to fill?

A2 hours
B1 hour 40 minutes
C24 minutes
D1 hour 20 minutes

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Answer: A) 2 hours

Rates per minute: fill

\frac{1}{40}

, drain

\frac{1}{60}

. Net

\frac{3 - 2}{120} = \frac{1}{120}

: 120 minutes = 2 hours.

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