Page 102 - ICSE Math 7

1 1 3 – 1 2 1
∴ Tank emptied by pipe Y in 1 hour = – = = –
8 24 24 24 12
1
∴ Time required by pipe Y to empty the full tank = 1/12 = 12 hours.

(b) Tank filled by both pipes in 1 hour = 1
24

∴ Amount of water filled in 1 hour = 1 × 400 litres = 50 litres
24 3

∴ Time required to fill 150 litres = 150 = 150 × 3 = 9 hours.
50/3 50

2 3
Example 25: A could paint of a wall in 8 days and B could paint of the same wall in 6 days.
3 4
They worked together for 4 days and then A left. The remaining work was done by B.
How much time did B take to finish the remaining work?
2
Solution: In 8 days A can paint of the wall.
3
1
2
∴ In 1 day A can paint 3 × 8 = 12 of the wall.
3
In 6 days B can paint of the wall.
4
1
∴ In 1 day B can paint 3 = of the wall.
4 × 6 8
1
∴ Work done by A and B together in 1 day = 1 + = 2 = 5
12 8 3 + 24 24
5 5
Thus, work done by A and B together in 4 days = 4 × =
5 1 24 6
∴ Work left = 1 – =
6 6
1
4
8
Time required by B to finish the remaining work = 1/6 = = = 1 days.
1/8 6 3 3
EXERCISE 7.4

1. Shahid can complete a work in 12 hours and Rahul can do the same work in 15 hours. How long
will they take to complete it if they work together?

2. A and B can together colour a painting in 20 minutes. A alone can colour the painting in 25
minutes. In how much time can B alone colour the painting?
3. A tap fills a tank in 9 hours. Another tap empties the full tank in 12 hours. How long will it take
to fill the tank, if both the taps are open?
4. Joseph and Alia can finish a science project in 18 hours and 15 hours respectively. Find:
(a) work done by Joseph in 6 hours.

(b) work left after Joseph has worked for 6 hours.
(c) time required by Alia to finish the remaining work.
5. A tank has two pipes X and Y. Pipe Y empties the tank. If only pipe X is open, then the empty
tank is filled in 14 hours and if both the pipes are open, then the tank is filled in 21 hours. In how
much time can the full tank be emptied if only pipe Y is open?

88