1. If a pipe can fill a tank in x hours, then:
part filled in 1 hour = 1/x
2.If a pipe can empty a tank in y hours, then:
part emptied in 1 hour = 1/y
3. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where y > x), then on opening both the pipes, then
the net part filled in 1 hour = 1/x1/y
4. If a pipe can fill a tank in x hours and another pipe can empty the full tank in y hours (where x > y), then on opening both the pipes, then
the net part emptied in 1 hour = 1/y1/x
1. 

Part of the tank filled by A in 1 minute = 1/12
Part of the tank filled by B in 1 minute = 1/18
Part of the tank filled by both the pipes in one minute = 1/12 + 1/18 = 5/36
∴ The tank can be filled in 36/5 minutes = 7.2 minutes
2. 

Work done by the 3 pipes together in 1 minute = 1/12 + 1/18 – 1/36 = 1/9
So, the empty tank will be filled in 9 minutes.
3. 

Work done by C in one minute.
Work done by C in one minute = (1/20 + 1/30) – 1/24 = 1/12 – 1/24 = 1/24
∴ C can empty the tank in 24 minutes.
4. 

Pipe B works for 15 min.
In 1 min B fills (1/30)th of the tank
in 15 min it fills 15 x (1/30) = 1/2
The remaining 1/2 is filled by A. since A fills the tank fully in 20 min, it takes 10 min to fill 1/2 of the tank.
Hence, A worked for 10 min. So, A should be closed after 10 minutes.
5. 

Work of A + B + C in 1 hour = 1/3
Remaining part of the tank = 1 – 1/3 = 2/3
Time taken by (A + B) to fill this (2/3)rd of the tank = 4 hours.
⇒ A and B together fill the tank in 6 hours.
Now, we know A + B + C = 3 hours
⇒ A + B = 6 hours
∴ C = 1/3 – 1/6 = 1/6
So, C alone can till the tank in 6 hours.
6. 

Work done by leak and the filling tap in 1 hour = 1/12
Work done by filling tap = 1/8 – 1/12 = 1/24
⇒ Tank can be filled in 24 hours.
∴ Capacity of tank = 24 x 60 x 4 = 5760 liters
7. 

Filling tap can fill (1/6)th of the tank in 1 hour.
Emptying tap can empty (1/12)th of the tank in 1 hour.
in 1 hour, the quantity of water filled by both the taps working together is
= 1/6 – 1/12 = (1/12)th of the tank.
∴ It takes 12 hours to completely fill the tank.
8. 

Tap A can fill (1/2) of the tank in 1 hour.
Tap B can fill (1/3) of the tank in 1 hour.
Tap A and tap B together fill (1/2 + 1/3) of the tank i. e. (5/6)th of the tank in 1 hour.
time taken by them to fill the tank = 1/(5/6) = 6/5 hours = 6/5 x 60 min = 72 min.
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