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Example 20: Mansi can do a piece of work in 20 days and Leena can do the same work in 25 days.
They work together for 5 days and then Mansi goes away. In how many days will Leena finish the
remaining work?
Solution: We have, Mansi can finish the work in 20 days and Leena can finish the work in 25 days.
1
So, Mansi’s 1 day’s work =
20
1 Quick Check
and Leena’s 1 day’s work =
25 1. Shyama alone can knit a
When they work together, their 1 day’s work sweater in 6 hours and Radha can knit
1 1 5 + 4 9 a sweater in 8 hours. How much time
= + = = would they take working together to
20 25 100 100
9 9 knit a sweater?
Therefore, (Mansi + Leena)’s 5 days’ work = 5 × 100 = 20 2. P, Q, and R together can do a piece of
9 11 work in 4 days. If P and Q can do the
So, remaining work = 1 − = work in 10 days and Q and R can do
20 20
The remaining work is to be completed by Leena whose it in 5 days.
1 (a) In how many days can Q alone do
1 day’s work = . the same work?
25 (b) In how many days can P and R
Now, 1 part of the work Leena does in 1 day. together do the same work?
25
11  11 1 
So, the remaining work is done by Leena in  ÷  days
20  20 25
 11  55 3
=

  20 × 25 days = 4 days = 13 4 days

Pipes and Cisterns
A cistern or a water tank is connected with two types of pipes. One that fills it up is called an
inlet; the other that empties it is called an outlet. While solving the problems related to pipes and
cisterns, we consider the work done by an inlet is always positive and the work done by the outlet
is always negative.
1
• If an inlet fills a tank in ‘n’ hours, then the part of the tank filled in 1 hour is .
n
• If an outlet empties a tank in ‘n’ hours, then the part of the tank emptied in 1 hour is – 1 .
n
Example 21: A cistern can be filled by tap A in 4 hours and by tap B in 5 hours. How long will it
take to fill it if both taps are opened together?
Solution: Time taken by the first tap to fill the cistern = 4 hours

Time taken by the second tap to fill the cistern = 5 hours
1
So, the part of the cistern filled by first tap in 1 hour = , and
4
the part of the cistern filled by second tap in 1 hour = 1
5
1 1 54 9
+
Therefore, the cistern filled by both the taps in 1 hour = + = =
4 5 20 20
20 2
Thus, both the taps together will fill the cistern in = 2 hours.
9 9

291 Direct and Indirect Variations