Page 143 - Maths Skills - 8

Direct and Inverse Proportions 141

Pipes and Cisterns
We follow some general rules for solving problems related to pipes and cisterns which are as follows:

(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 in
1  −  1
1 hour is , or the work done by the outlet in 1 hour is .
y  
 y

Let us learn through examples.

Let’s Attempt

Example 1: A tap can fill up an empty tank in 6 hours. Another tap can empty it in 8 hours. How long will it take
to fill the empty tank if both the inlet and outlet taps are turned on together?

Solution: Time taken by the first tap to fill up an empty tank = 6 hours.

Time taken by the second tap to empty it = 8 hours

1 1
Work done by the first tap in 1 hour = and, work done by the second tap in 1 hour =
6 8

1
 =
Work done by both the taps in 1 hour = 1 +− 1 1 - = 43- = 1

6  8 6 8 24 24
Thus, the tank will be filled up in 24 hours, when both the taps are turned on together.
Example 2: A cistern can be filled by one tap in 5 hours and by another tap in 3 hours. If both the taps are turned
on together, how long will it take to fill it?

Solution: Time taken by the first tap to fill the cistern = 5 hours.
Time taken by the second tap to fill the cistern = 3 hours.

1 1
Work done by the first tap in 1 hour = and, work done by the second tap in 1 hour =
5 3
1
Work done by both the taps in 1 hour = 1 + = 35+ = 8
5 3 15 15
Thus, both the taps will fill the cistern together in 15 hours.
8
Example 3: Two inlet taps can fill up an empty tank in 10 hours and 15 hours respectively. An outlet tap can
empty the full tank in 8 hours. If all the taps are turned on together, find in how much time will the
empty tank be filled up completely?

Solution: Time taken by the first inlet tap to fill up an empty tank = 10 hours.
Time taken by the second inlet tap to fill up an empty tank = 15 hours

Time taken by an outlet tap to empty it completely = 8 hours.

1
First inlet tap’s 1 hour’s work =
10