Question

Two pipes A and B can separately fill a cistern in 40minutes and 30minutes 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 20minutes.in how much time the third pipe alone can empty the cistern?

Answer 1

Answer:

Quantitative Aptitude ≫ Time and Work ≫ Pipe and Cistern

Question:

Two pipes A and B can fill a cistern in 37.5 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

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Options:

5 minutes

9 minutes

10 minutes

15 minutes

Correct Answer: Option 2 (Solution Below)

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Solution:

Given:

PipeA can fill the tank in 37.5 minutes

PipeB can fill the tank in 45 minutes

A cistern is filled in 1/2 hour i.e. 30 minutes

Formula Used:

The capacity of cistern = LCM of time taken by PipeA and PipeB

The efficiency of Pipe = Capacity of cistern/time taken to fill the cistern

Calculation:

The capacity of cistern = LCM of time taken by PipeA and PipeB

⇒ The capacity of cistern = LCM of 37.5 minutes and 45 minutes

⇒ The capacity of cistern = 225 units

The efficiency of Pipe = Capacity of cistern/time taken to fill the cistern

⇒ The efficiency of PipeA = Capacity of cistern/time taken to fill the cistern by PipeA

⇒ The efficiency of PipeA = 225/37.5

⇒ The efficiency of PipeA = 6

The efficiency of PipeB = Capacity of cistern/time taken to fill the cistern by PipeB

⇒ The efficiency of PipeB = 225/45

⇒ The efficiency of PipeB = 5

The cistern filled in just half an hour

⇒ PipeA runs for 30 minutes

⇒ 6× 30 = 180 units

i.e. 180 units filled by PipeA in 30 minutes

Remaining cistern filled by B,

⇒ Remaining quantity = 225 - 180

⇒ Remaining quantity = 45 units

To fill the 45 units PipeB will have to run for,

⇒ Quantity/ Efficiency of PipeB = total time taken by PipeB

⇒ total time taken by PipeB = 45/5

⇒ total time taken by PipeB = 9 minutes

∴ PipeB is turned off after 9 minutes