Pipes & Cistern Questions and Answers

Answer: D

Let the capacity of the pool be LCM(20, 30) = 60 units.
=> Efficiency of pipe A = 60 / 20 = 3 units / minute
=> Efficiency of pipe B = 60 / 30 = 2 units / minute
=> Combined efficiency of pipe A and pipe B = 5 units / minute
Now, the pool is filled with the efficiency of 5 units / minute for two minutes.
=> Pool filled in two minutes = 10 units
=> Pool still empty = 60 - 10 = 50 units
This 50 units is filled by B alone.
=> Time required to fill these 50 units = 50 / 2 = 25 minutes
 
Therefore, total time required to fill the pool = 2 + 25 = 27 minutes

Answer: A

Let the capacity of the tank be LCM (20, 12) = 60 units
=> Efficiency of A working alone = 60 / 20 = 3 units / hour
=> Efficiency of A and B working together = 60 / 12 = 5 units / hour
Therefore, Efficiency of B working alone = Efficiency of A and B working together - Efficiency of A working alone
=> Efficiency of B working alone = 5 - 3 = 2 units / hour
=> Time required by B alone to drain the tank = 60 / 2 = 30 hours
 
But we are given that B can drain the tank at the rate of 20 liters per hour.
Therefore, capacity of the water tank = 20 x 30 = 600 liters
 

Answer: B

Let the capacity of the pool be LCM (10, 20, 15) = 60 units.
=> Efficiency of pipe A = 60 / 10 = 6 units / hour
=> Efficiency of pipe B = 60 / 20 = 3 units / hour
=> Efficiency of pipe C = 60 / 15 = 4 units / hour
 
=> Efficiency of pipe A and pipe C working together = 10 units / hour
=> Efficiency of pipe B and pipe C working together = 7 units / hour
 
=> Pool filled in first hour = 10 units
=> Pool filled in second hour = 7 units
=> Pool filled in 2 hours = 10 + 7 = 17 units
 
We will have 3 cycles of 2 hours each such that A and C, and, B and C work alternatively.
=> Pool filled in 6 hours = 17 x 3 = 51 units
=> Pool empty = 60 - 51 = 9 units
Now, these 9 units would be filled by A and C working together with the efficiency of 10 units / hour.
=> Time required to fill these 9 units = 9/10 hour = 0.9 hours = 54 minutes
 
Therefore, total time required to fill the pool = 6 hours 54 minutes
 

Answer: D

If A can fill a tank in x hours and B can fill a tank in y hours. Then the tank will be filled (empty) in = (xy / y-x) hours
Time taken by A = 9 hours
Time taken by B = 10 hours
Time taken by A and B = (9×10 / 10-9) = 90 hours.
 

Answer: B

Let the capacity of the cistern be LCM(12, 15, 20, 30) = 60 units.
=> Efficiency of pipe A = 60 / 12 = 5 units / minute
=> Efficiency of pipe B = 60 / 15 = 4 units / minute
=> Efficiency of pipe C = 60 / 20 = 3 units / minute
=> Efficiency of pipe D = 60 / 30 = 2 units / minute
=> Combined efficiency of pipe A, pipe B, pipe C and pipe D = 10 units / minute
 
Therefore, time required to fill the cistern if all the pipes are opened simultaneously = 60 / 10 = 6 minutes

Answer: B

In this type of questions we first get the filling in 1 minute for both pipes then we will add them to get the result, as

Part filled by A in 1 min = 1/20

Part filled by B in 1 min = 1/30

Part filled by (A+B) in 1 min = 1/20 + 1/30

= 1/12

So both pipes can fill the tank in 12 mins.

Answer: C

When we have question like one is filling the tank and other is empting it, then we subtraction as,

Filled in 1 hour = 1/4

Empties in 1 hour = 1/9

Net filled in 1 hour = 1/4 - 1/9

= 5/36

So cistern will be filled in 36/5 hours i.e. 7.2 hours

Answer: D

Half tank will be filled in 3 hours

Lets calculate remaining half,

Part filled by the four taps in 1 hour = 4 × (1/6) = 2/3

Remaining part after 1/2 filled = 1-1/2 = 1/2

Total time = 3 hours + 45 mins = 3 hours 45 mins

Answer: A

There are two important points to learn in this type of question,

First, if both will open then tank will be empty first.

Second most important thing is,

If we are calculating filling of tank then we will subtract as (filling-empting)

If we are calculating empting of thank then we will subtract as (empting-filling)

So lets come on the question now,

Part to emptied 2/5

Part emptied in 1 minute =

1/6 - 1/10 = 1/15 => 1/15 : 25 :: 1: x =>25 × 15 = 6mins

Answer: D

Part filled by A in 1 hour = 1/5

Part filled by B in 1 hour = 1/10

Part filled by C in 1 hour = 1/30

Part filled by (A+B+C) in 1 hour =

So all pipes will fill the tank in 3 hours.