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 Pipes and Cistern Questions

Popular Latest Rated Important Formulae

FACTS  AND  FORMULAE  FOR  PIPES  AND  CISTERN  QUESTIONS

 

 

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

 

2. Outlet : A pipe connected with a tank or cistern or 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 empty 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, then the net part filled in 1 hour = 1x-1y

(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 = 1y-1x

Q:

Two pipes A and B can separately fill a cistern in 60 min and 75 min respectively. There is a third pipe in the bottom of the cistern to empty it. If all the three pipes are simultaneously opened, then the cistern is full in 50 min. In how much time, the third pipe alone can empty the cistern ?

A) 85 min B) 95 min
C) 105 min D) 100 min
 
Answer & Explanation Answer: D) 100 min

Explanation:

Work done by the third pipe in 1 min = 1/50 - (1/60 + 1/75) = - 1/100.
[-ve sign means emptying]

The third pipe alone can empty the cistern in 100 min.

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7 8049
Q:

Pipe K fills a tank in 30 minutes. Pipe L can fill the same tank 5 times as fast as pipe K. If both the pipes were kept open when the tank is empty, how much time will it take for the tank to overflow ?

A) 3 minutes B) 2 minutes
C) 4 minutes D) 5 minutes
 
Answer & Explanation Answer: D) 5 minutes

Explanation:

Let the total capacity of tank be 90 liters.
Capacity of tank filled in 1 minute by K = 3 liters.
Capacity of tank filled in 1 minute by L = 15 liters.
Therefore, capacity of the tank filled by both K and L in 1 minute = 18 liters.
Hence, time taken by both the pipes to overflow the tank = 90/18 = 5 minutes.

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11 7759
Q:

A water tank in a village is normally filled in 8 hours but takes 2 hours longer to fill because of a leak in its bottom. If the tank is full, in how many hrs will the leak empty it ? 

A) 34 hrs B) 36 hrs
C) 38 hrs D) 40 hrs
 
Answer & Explanation Answer: D) 40 hrs

Explanation:

The time taken by the leak to empty the tank = 18 - 110 = 5 - 440 = 140

Therefore, the leak empties the tank in 40 hours.

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10 7062
Q:

A Tank is normally filled in 9 hours but takes four hours longer to fill because of a leak in its bottom. If the tank is full, the leak will empty it in ?

A) 32.5 hrs B) 29.25 hrs
C) 30.30 hrs D) 31 hrs
 
Answer & Explanation Answer: B) 29.25 hrs

Explanation:

Let the leak will empty the tank in x hrs 

Then, 1/9 - 1/x = 1/13

x = 29.25 hrs

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10 6823
Q:

A tap can fill a tank in 6 hours. After half the tank is filled three more similar taps are opened. What is the total time taken to fill the tank completely ?

A) 4 hrs 15 min B) 3 hrs 24 min
C) 4 hrs 51 min D) 3 hrs 45 min
 
Answer & Explanation Answer: D) 3 hrs 45 min

Explanation:

Time taken by one tap to fill half of the tank = 3 hrs.

Part filled by the taps in 1 hour = 4 x 1/6 = 2/3

Remaining part = 1 - 1/2 = 1/2

2/3 : 1/2 :: 1 : p

p = 1/2 x 1 x 3/2 = 3/4 hrs. i.e., 45 min

So, total time taken = 3 hrs 45 min.

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13 6510
Q:

The ratio of efficiencies of two filling pipes is 4 : 5. There is a third emptying pipe which efficiency is two third of the average efficiency of first two filling pipes can empty a filled tank in 36 minutes. In how much time both the filling pipes can fill the tank when it is empty?

A) 16 min B) 12 min
C) 14 min D) 20 min
 
Answer & Explanation Answer: B) 12 min

Explanation:

Let the efficiencies of filling pipes is 4p and 5p respectively.

Efficiency of pipe which empty the tank = 2/3 x 9p/2 = 3p

Total work = 3p x 36 = 108p

 

Time to fill the tank by both the pipes = 108p/9p = 12 min.

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Q:

A tank is filled in eight hours by three pipes K, L and M. Pipe K is twice as fast as pipe L, and L is twice as fast as M. How much time will pipe L alone take to fill the tank ?

A) 32 hrs B) 24 hrs
C) 28 hrs D) 26 hrs
 
Answer & Explanation Answer: C) 28 hrs

Explanation:

1/K + 1/L + 1/M = 1/8 (Given)
Also given that K = 2L and L = 2M
=> 1/2L + 1/L + 2/L = 1/8
=> (1 + 2 + 4)/2L = 1/8
=> 2L/7 = 8
=> L = 28 hours.

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8 5582
Q:

The capacity of a tank is 2400 m3.  A pump can be used both for filling and emptying the tank.  The emptying capacity of the pump is 10 m3/minute higher than its filling capacity. And also, the pump needs 8 minutes less to empty the tank than to fill it. Find the filling capacity of the pump. 

A) 46 cub.m/min B) 44 cub.m/min
C) 48 cub.m/min D) 50 cub.m/min
 
Answer & Explanation Answer: D) 50 cub.m/min

Explanation:

Let filling capacity of the pump be 'F' m3/min

Then, the filling capacity of the pump will be (F + 10) m3/min

From the given data,

2400F - 2400F+10= 8⇒ 2400 F+10-FF(F+10) =8⇒ F2 + 10F - 3000 = 0⇒ F = 50 m3/min

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