Page 101 - ICSE Math 7

Time and Work
Maths Info
We solve problems based on time and work using the following:
1 Full work is taken as 1.
One day’s work =
Number of days required to complete the work

Number of days required to complete the work = 1
One day’s work
Time required to do a certain work = Work to be done
Work done in unit time
Example 22: A and B can complete a piece of work in 20 days and 30 days respectively.

(a) How long will they take to complete the work together?
1
(b) In how much time will they complete of the work?
3
Solution: (a) A can complete the work in 20 days.
1
∴ A’s one day’s work =
20 1
Similarly, B’s one day’s work =
30
A and B’s one days work, when they work together = 1 + 1 = 30 + 20 = 50 = 5
20 30 60 60 6
1 6 1
Thus, A and B will together complete the work in = = 1 days.
5/6 5 5
1 1/3 1 6 2
(b) Time required to do of the work = = × = days.
3 5/6 3 5 5
Example 23: Rahul and Simran together can finish a project in 15 days. Rahul alone can finish it in
20 days. In how much time can Simran alone finish the project?
Solution: Rahul and Simran together finish the project in 15 days.
1
∴ Rahul and Simran’s one day’s work =
15
Rahul alone can finish the project in 20 days.
1
∴ Rahul’s one day’s work =
20
1 1 4 – 3 1
∴ Simran’s one day’s work = – = =
15 20 60 60
1
Thus, Simran will finish the project in = 60 days.
1/60
Example 24: A tank of capacity 400 litres can be filled by pipe X in 8 hours. The same tank can be
emptied by pipe Y. If both the pipes are opened, then the tank is filled in 24 hours. Find:
(a) the time required by pipe Y to empty the full tank.
(b) the time required to fill 150 litres if both the pipes are open.
Solution: (a) Pipe X can fill the tank in 8 hours.
1
∴ Tank filled by pipe X in 1 hour =
8
When both the pipes are open, tank is filled in 24 hours.

∴ Tank filled by both pipes in 1 hour = 1
24

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