Pipes and Cisterns PRACTICE SET 1 FOR RRVUNL AE & JE,UPPCL AE,DMRC/NMRC,SSC JE,BSPHCL JE

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 a cistern or a reservoir, emptying it, is known
as an outlet.

1. If a pipe
can fill a tank in α hours, then: part filled in 1 hour = 1/α

2. If a pipe
can empty a full tank in β hours,
then: part emptied in 1 hour = 1/β

3. If a pipe
can fill a tank in α hours and another pipe can empty the full tank in β hours (where
β> α), then on
opening both the pipes,
The net part
filled in 1 hour = (1/α) – (1/β)

4. If a pipe
can fill a tank in α hours and another pipe can empty the full tank in β hours (where α > β), then on
opening both the pipes,
The net part
emptied in 1 hour = (1/β) – (1/α)

Also, these shortcut formulas can be
used:

1. If a pipe
can fill a tank in α hours and another pipe can empty the full tank in β hours (where
β> α), then time
taken to fill the tank, when both the pipe are opened, αβ/(β – α)

2. If a pipe
can fill a tank in α hours and another pipe can fill the same tank in β hours,
then the net part the time taken to fill, when both the pipes are open

Time taken
to fill the tank = αβ/(α + β)

3. If a pipe
fills a tank in α hour and another fills the same tank in β hours, but a third
one empties the full tank in ɣ hours, and all of them are opened together, then

Time taken
to fill the tank = αβɣ/(βɣ +αɣ – αβ)

4. A pipe
can fill a tank in α hours. Due to a leak in the bottom, it is filled in β
hours. The time taken by the leak to empty the tank is, αβ/(β – α)

Example: 01

Two pipes A and B can fill the tank in 30
hrs and 45 hrs respectively. If both the pipes are opened simultaneously, how
much time will be taken to fill the tank?

Solution:

By 1st method;

A fills the
tank in 1 hr = 1/30 parts

B fills the
tank in 1 hr = 1/45 parts

A and B
together fills the tank in 1 hr = 1/30 + 1/45 = 1/18 parts

So, time
required to fill the tank is 18 hrs.

By 2nd method; Time taken = αβ/(α + β)
= (30 × 45)/(30 + 45) = 18 hrs.

Example: 02

Pipe A can fill a tank in 25 hrs while B
alone can fill it in 30 hrs and C can empty the full tank in 45 hrs. If all the
pipes are opened together, how much time will be needed to make the tank full?

Solution:

The tank
will be full in = (25 × 30 × 45)/[(30 × 45) + (25 × 45) – (25 × 30)] = 19.56
hours.

Example: 03

Two pipes A and B would fill a cistern in
24 hrs and 32 hrs respectively. If both the pipes are opened together; find
when the first pipe must be turned off so that the cistern may be just filled
in 16 hrs.

Solution:

B fills the
tank in 1 hr = 1/32 parts

B fills the
tank in 16 hrs = 16/32 parts = 1/2 part.

Given,

A fill the full
tank in 24 hrs

Therefore, A
fills the 1/2 part in just 12 hrs.

Alternate Method: The first should work
for = [1 – (16/32)] × 24 = 12 hrs.

 

SOLVED EXAMPLES