Page 106 - ICSE Math 8

Pipes and Cisterns

Given below are some general rules for solving problems related to pipes and cisterns:
(i) If a pipe fills a tank/cistern in x hours, then the part of the tank/cistern
1 1
filled in 1 hour is , or the work done by the inlet in 1 hour is .
x x
(ii) If a pipe empties a full tank in y hours, then the part of the tank emptied

1  −  1
in 1 hour is , or the work done by the outlet in 1 hour is   .
y  y 
Example 12: A pipe can fill a cistern is 5 hours. The cistern can be emptied by an outlet pipe in 6 hours.
How much time will it take to fill the cistern if both the pipes are opened together?

Solution: The inlet pipe can fill the cistern in 5 hours.
1
\ In 1 hour, the pipe fills of the cistern.
5
The outlet pipe can empty the cistern in 6 hours.
1
\ In 1 hour, the pipe empties of the cistern.
6
 1 1 65 1
−
\ In 1 hour,   5 − 6  = 30 = 30 of the cistern will be filled.
1 30
\ The cistern will be filled in 1 ÷ = 1 × = 30 hours
30 1
Example 13: A Tank can be filled by two taps A and B in 6 and 8 hours respectively. The full Tank can be
emptied by a third tap C in 4 hours. If all the taps are turned on at the same time, find the time
taken to fill the empty tank.
Solution: Tap A fills the tank in = 6 hours
1
Tap A fills in 1 hr = tank …(i)
6
Tap B fill the tank in 8 hours
1
Tap B fills in 1 hr = tank …(ii)
8
Tap C empties the tank in = 4 hours
1
Tap C empties in 1 hour = … (iii)
4
From equation (i), (ii) and (iii) we get

1 1 1 4 + 3 – 6 1
∴ (A + B + C) fill in 1 hour = + + tank = =
6 8 4 24 24
∴ (A + B + C) fill the tank in = 24 hours
All the taps turned on the same time the tank will fill in 24 hours.

EXERCISE 9.3

1. Minti can do a piece of work in 12 days. Minti and Rinki together can finish the work in 8 days.
Find: (a) the number of days in which Rinki alone can finish the work.
(b) the work left if Rinki alone works on it for 4 days.
2. 10 workers earn ` 48,000 in 4 days. What amount will 8 workers earn in 6 days?
3. Arushi and Devesh are making a painting. Arushi can complete the painting in 30 minutes. Both Arushi
and Devesh can complete the painting together in 20 minutes. They work together for 10 minutes Arushi
goes away. In how many minutes will Devesh finish the painting?

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