MathsICSE Class 8 · Time and Work

Pipes and Cisterns, and Sharing Wages by Work Done (ICSE Class 8 Maths)

Updated 17 October 2026 · Fact-checked

An inlet pipe that fills a tank in $a$ hours fills $\frac{1}{a}$ of it per hour; an outlet that empties it in $b$ hours removes $\frac{1}{b}$ per hour, so the net rate is $\frac{1}{a} - \frac{1}{b}$. Wages are shared in the ratio of the work done by each worker.

Add the inlet rate and subtract the outlet rate to get the net rate; wages follow the work done, so the faster worker gets more.

Illustration drawn for QuestionBuddy.

Understand Pipes and Cisterns and Sharing Wages

Pipes and cisterns are time-and-work problems with a tank as the job.

Inlet and outlet. An inlet (tap, pipe) fills; an outlet (waste pipe, leak) empties. If an inlet fills the full tank in $a$ hours it does $+ \frac{1}{a}$ per hour; if an outlet empties the full tank in $b$ hours it does $- \frac{1}{b}$ per hour.

Net rate. Add signed rates for all pipes open together:
$ $net per hour = \sum \frac{1}{a _{i}} - \sum \frac{1}{b _{j}} .$ $
If the net is positive the tank fills in $\frac{1}{net}$ hours. If negative, it empties.

Leak. A leak is an outlet. If a pipe alone fills the tank in $6$ h but with the leak it takes longer, the leak's rate is the difference of the two rates.

Closing a pipe midway. Compute the fraction filled with the first set of pipes, then use the new net rate for the remaining fraction.

Sharing wages. When workers are paid together, divide the total in the ratio of the work done, not the days taken. If $A$ and $B$ work together for the same time, the ratio of their wages is the ratio of their one-day works: $\frac{1}{a} : \frac{1}{b} = b : a$ . The worker who would take less time alone earns more.

Checking. Wages must add up to the total, and the faster worker's share must be larger.

Pipes and Cisterns and Sharing Wages: formulas to remember

Inlet rate: $+ \frac{1}{a} per hour$; Fills the tank in $a$ hours alone.
Outlet rate: $- \frac{1}{b} per hour$; Empties the tank in $b$ hours alone.
Wage ratio (same time worked): $\frac{1}{a} : \frac{1}{b} = b : a$; Faster worker gets more.

How to solve Pipes and Cisterns and Sharing Wages questions

Give each pipe a signed hourly rate, add them, and use the reciprocal.

1Write each pipe's rate as a signed fraction of the tank per hour.
2Add the rates of the pipes that are open together.
3Take the reciprocal of the net rate for the time.
4For a pipe closed midway, find the fraction filled first, then the remaining time.
5For wages, divide in the ratio of work done and check the total.

Pipes and Cisterns and Sharing Wages in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Leaking water tank

Suppose a tap fills a tank in 6 hours, but a leak at the bottom could empty the full tank in 8 hours.

How long does the tank take to fill with the leak?

Try it first, then show the solutionSolution

Net rate $= \frac{1}{6} - \frac{1}{8} = \frac{4 - 3}{24} = \frac{1}{24}$ .

Answer: 24 hours.

Memory hook: A leak is a pipe with a minus sign.

Tricks to remember Pipes and Cisterns and Sharing Wages

Short memory aids. Say each one aloud once, then use it on a question the same day.

Plus for fill, minus for drain
Write +1/a for inlets and -1/b for outlets before adding.
Use it when: Mixed pipes.
Faster earns more
Wages follow work done: the one who needs fewer days alone gets the bigger share.
Use it when: Sharing wages.

Pipes and Cisterns and Sharing Wages: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Inlet and outlet · 1 mark · MCQBoard level

An inlet pipe fills a tank in 6 hours and an outlet empties it in 12 hours. Open together, the tank fills in:
(a) 4 h (b) 6 h (c) 12 h (d) 18 h

Try it first, then show the solutionSolution

Net $= \frac{1}{6} - \frac{1}{12} = \frac{1}{12}$ , so 12 hours.

Answer: (c)

Example 2: Two taps · 3 marks · Short answerBoard level

Tap A fills a tank in 20 minutes and tap B in 30 minutes. How long do they take together?

Try it first, then show the solutionSolution

$\frac{1}{20} + \frac{1}{30} = \frac{3 + 2}{60} = \frac{1}{12}$ .
Time $= 12$ minutes.

Answer: 12 minutes

Example 3: Tank with a leak · 3 marks · Short answerHarder board level

A pipe fills a tank in 6 hours, but a leak can empty the full tank in 8 hours. In how many hours will the tank fill with the leak present?

Try it first, then show the solutionSolution

Net rate $= \frac{1}{6} - \frac{1}{8} = \frac{4 - 3}{24} = \frac{1}{24}$ .
The tank fills in 24 hours.

Answer: 24 hours

Example 4: Sharing wages · 4 marks · Short answerHarder board level

A can finish a job in 12 days and B in 24 days. They work together to finish it and are paid Rs 1,800 in all. Find the share of each.

Try it first, then show the solutionSolution

Together they take $\frac{1}{\frac{1}{12} + \frac{1}{24}} = 8$ days.
A does $\frac{8}{12} = \frac{2}{3}$ , B does $\frac{8}{24} = \frac{1}{3}$ . Ratio $2 : 1$ .
A gets $\frac{2}{3} \times 1800 = 1200$ ; B gets $600$ .

Answer: A Rs 1,200; B Rs 600

Example 5: Closing a pipe midway · 4 marks · Long answerHOTS / competency

Pipes A and B fill a tank in 12 h and 15 h respectively, and pipe C empties it in 20 h. All three are opened together; after 4 hours C is closed. Find the total time taken to fill the tank.

Try it first, then show the solutionSolution

Net with all three: $\frac{1}{12} + \frac{1}{15} - \frac{1}{20} = \frac{5 + 4 - 3}{60} = \frac{1}{10}$ .
In 4 h: $\frac{4}{10} = \frac{2}{5}$ filled; remaining $\frac{3}{5}$ .
A and B together: $\frac{1}{12} + \frac{1}{15} = \frac{9}{60} = \frac{3}{20}$ per hour.
Time for the rest $= \frac{3/5}{3/20} = 4$ h. Total $= 4 + 4 = 8$ hours.

Answer: 8 hours

Where students lose marks in Pipes and Cisterns and Sharing Wages

The slips examiners see most often, and what to write instead.

Mistake: Adding the outlet rate to the inlet rate
An outlet works against the inlet.
Wrong working
Net $= \frac{1}{6} + \frac{1}{8} = \frac{7}{24}$ .
Right working
Net $= \frac{1}{6} - \frac{1}{8} = \frac{1}{24}$ .
Do this: Write the sign before each fraction.
Usually costs: Answer mark.
Mistake: Sharing wages in the ratio of days
The worker who takes more days does less work per day and earns less.
Wrong working
A 12 days, B 24 days: wages $12 : 24 = 1 : 2$ .
Right working
Ratio of work is $\frac{1}{12} : \frac{1}{24} = 2 : 1$ .
Do this: Invert the days to get work.
Usually costs: Both shares marks.

Exam tips

Write "+" or "-" next to every pipe rate.
Check the answer: filling time with a leak is longer than without.
Wage shares must add to the total paid.

Practice questions on Pipes and Cisterns and Sharing Wages

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
A tap fills a tank in 4 hours. The part filled in 1 hour is:
(a) $\frac{1}{4}$ (b) $4$ (c) $\frac{3}{4}$ (d) $\frac{1}{2}$
Hint
Fraction per hour.
Answer
(a)
Q2 · 2 marks · Short answerBoard level
An inlet pipe fills a tank in 8 hours and an outlet empties it in 10 hours. Both are opened together. How long to fill the tank?
Hint
Net rate is positive.
Answer
$\frac{1}{8} - \frac{1}{10} = \frac{5 - 4}{40} = \frac{1}{40}$ ; 40 hours.
Q3 · 3 marks · Short answerHarder board level
Two taps fill a tank in 24 minutes and 40 minutes. How long do they take together?
Hint
$\frac{1}{24} + \frac{1}{40}$ with LCM 120.
Answer
$\frac{5 + 3}{120} = \frac{1}{15}$ ; 15 minutes.
Q4 · 3 marks · Short answerHarder board level
A can do a job in 10 days and B in 15 days. They work together for 6 days and are paid Rs 2,500. How should it be shared?
Hint
Ratio of rates 1/10 : 1/15.
Answer
Ratio $= \frac{1}{10} : \frac{1}{15} = 3 : 2$ . A gets Rs 1,500 and B Rs 1,000.
Q5 · 4 marks · Long answerHOTS / competency
Pipes A and B can fill a tank in 6 h and 9 h; pipe C can empty it in 18 h. All three are opened at 8 am and C is closed at 11 am. At what time is the tank full?
Hint
Find the fraction filled by 11 am.
Answer
Net with all: $\frac{1}{6} + \frac{1}{9} - \frac{1}{18} = \frac{3 + 2 - 1}{18} = \frac{2}{9}$ . In 3 h: $\frac{2}{3}$ . Remaining $\frac{1}{3}$ at $\frac{1}{6} + \frac{1}{9} = \frac{5}{18}$ : $\frac{1/3}{5/18} = \frac{6}{5}$ h $= 1$ h $12$ min. The tank is full at 12:12 pm.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Net rate of an inlet (a h) and outlet (b h)?Show answer
1/a - 1/b.
2.A leak acts like what?Show answer
An outlet pipe.
3.Wages for workers on the same job are shared in what ratio?Show answer
The ratio of work done.
4.Pipe A fills in 6 h. Part in 2 h?Show answer
1/3.

Pipes and Cisterns and Sharing Wages: frequently asked questions

Can the net rate be zero?

Yes if 1/a = 1/b: the tank never fills or empties.

What if an outlet is faster than the inlet?

The net rate is negative and the full tank empties in the reciprocal of its magnitude.