IMPORTANT FORMULAS : PIPES AND CISTERN

Inlet:
A pipe connected with a tank or a cistern or a reservoir, that fills it, is known as an inlet.

Outlet:
A pipe connected with a tank or cistern or reservoir, emptying it, is known as an outlet.
If a pipe can fill a tank in x hours, then:
part filled in 1 hour = 1/x
If a pipe can empty a tank in y hours, then:
part emptied in 1 hour = 1/y
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/x - 1/y)
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/y - 1/x)

SOME SOLVED NUMERICAL ON PIPE AND CISTERN

.	Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes, and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical solutions P,Q and R respectively. What is the proportion of the solution R in the liquid in the tank after 3 minutes?
	A. 5 11 B. 6 11 C. 7 11 D. 8 11 Answer & Explanation Answer: Option B Explanation: Part filled by (A + B + C) in 3 minutes = 3 1 + 1 + 1 = 3 x 11 = 11 . 30 20 10 60 20 Part filled by C in 3 minutes = 3 . 10  Required ratio = 3 x 20 = 6 . 10 11 11

2.	Pipes A and B can fill a tank in 5 and 6 hours respectively. Pipe C can empty it in 12 hours. If all the three pipes are opened together, then the tank will be filled in:
	A. 1 13 hours 17 B. 2 8 hours 11 C. 3 9 hours 17 D. 4 1 hours 2 Answer & Explanation Answer: Option C Explanation: Net part filled in 1 hour 1 + 1 - 1 = 17 . 5 6 12 60  The tank will be full in 60 hours i.e., 3 9 hours. 17 17

3.	A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 hours to fill the tank. The leak can drain all the water of the tank in:
	A. 4 1 hours 3 B. 7 hours C. 8 hours D. 14 hours Answer & Explanation Answer: Option D Explanation: Work done by the leak in 1 hour = 1 - 3 = 1 . 2 7 14  Leak will empty the tank in 14 hrs.

4.	Two pipes A and B can fill a cistern in 37 minutes and 45 minutes respectively. Both pipes are opened. The cistern will be filled in just half an hour, if the B is turned off after:
	A. 5 min. B. 9 min. C. 10 min. D. 15 min. Answer & Explanation Answer: Option B Explanation: Let B be turned off after x minutes. Then, Part filled by (A + B) in x min. + Part filled by A in (30 -x) min. = 1.  x 2 + 1 + (30 - x). 2 = 1 75 45 75 11x + (60 -2x) = 1 225 75  11x + 180 - 6x = 225.  x = 9.

5.

A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same time during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe is:

A. 6 hours B. 10 hours C. 15 hours D. 30 hours Answer & Explanation Answer: Option C Explanation: Suppose, first pipe alone takes x hours to fill the tank . Then, second and third pipes will take (x -5) and (x - 9) hours respectively to fill the tank. 1 + 1 = 1 x (x - 5) (x - 9) x - 5 + x = 1 x(x - 5) (x - 9)  (2x - 5)(x - 9) = x(x - 5)  x2 - 18x + 45 = 0 (x - 15)(x - 3) = 0  x = 15.    [neglecting x = 3]