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## Pipes and Cisterns -> IMPORTANT FACTS AND FORMULAE

 Inlet : A pipe connected with a tank or a certain or a reservoir, that fills it, is known as an inlet. Outlet : A pipe connected with a tank or a cistern or a reservoir, emptying it, is known as an outlet. I. If a pipe can fill a tank in x hours, then : part filled in 1 hour = 1 / x. II. If a pipe can fill a tank in y hours, then : part emptied in 1 hour = 1 / y. III. 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, the net part filled in 1 hour = (1/x - 1/y). IV. 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, the net part emptied in 1 hour = (1/y - 1/x).

## Pipes and Cisterns -> SOLVED EXAMPLES

1. Two pipes A and B can fill a tank in 36 hours and 45 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? Sol. Part filled by A in 1 hour = 1 / 36; Part filled by B in 1 hour = 1 / 45; Part filled by (A + B) in 1 hour = (1 / 36 + 1 / 45) = 9 / 180 = 1 / 20.

## Pipes and Cisterns -> EXERCISE

1. A pump can fill a tank with a water in 2 hours. Because of a leak, it took 2x1/3 hours to fill the tank. The leak can drain all the water of the tank in

• A. 5 hrs
• B. 7 hrs
• C. 12 hrs
• D. 14 hrs
 Ans: D. Sol. Work done by the leak in 1 hour = (1/2 - 3/7) = 1/14. ∴ Leak will empty the tank in 14 hrs.

2. A leak in the bottom of a tank can empty the full tank in 8 hours. An inlet pipe fills water at the rate of 6 litres a minute. When the tank is full, the inlet is opened and due to the leak, the tank is empty in 12 hours. How many litres does the cistern hold?

• A. 7580
• B. 7960
• C. 8290
• D. 8640
 Ans: D. Sol. Work done by the inlet in 1 hour = (1/8 - 1/12) = 1/24. Work done by the inlet in 1 hour = (1/24 x 1/60) = 1/1440. ∴ Volume of 1/1440 part = 6 litres. ∴ Volume of whole = (1440 x 6) litres = 8640 litres.

3. 12 buckets of water fill a tank when the capacity of each tank is 13.5 litres. How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 litres?

• A. 18
• B. 15
• C. 16
• D. 12
 Ans: A. Sol. Capacity of each bucket = 9 litres. Number of buckets needed = (162/9) = 18.