A tank has both an inlet pipe and an outlet pipe. Working

Question

A tank has both an inlet pipe and an outlet pipe. Working alone, the inlet pipe can fill up the tank in 5 hours. Working alone, the outlet pipe can empty out the tank in 15 hours. If it is desired that the tank should be filled, from empty, exactly 6 hours after the inlet pipe is turned on at 9:30am, then at what time should the outlet pipe be opened ?

A) 10:00am

B) 10:45am

C) 12:00pm

D) 12:30pm

E) 1:30pm

I do not have the OA with me right now .

A. 10:00am
B. 10:45am
C. 12:00pm
D. 12:30pm
E. 1:30pm

Bunuel · Accepted Answer

In 6 hours the inlet pipe will pump in water equal to 6*1/5 = 6/5 of the pool. So, 1/5 more than necessary, which should be compensated by the outlet pipe. To pump out 1/5 of the water the outlet pipe needs 15/5 = 3 hours.

Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 3 hours = 12:30pm.

Answer: D.

HKHR · Answer

Bunuel, but to pump out the excess 1/5 of water, should we not use the combined rate (inflow+outflow)? The combined rate would be 10l outflow/hour. So time required will be 10/5 = 2 hours.

Therefore, the outlet pipe should be opened at 9:30am + 6 hours - 2 hours = 1:30pm. Any mistake here?

CrackverbalGMAT · Answer

Let us say that the capacity of the tank is 30 liters

Inlet --- 6 liters per hour
Outlet - 2 liters per hour

Let us say it should be turned on after x hours. Total time taken to fill 6 hours

6x + (4)(6-x) = 30
6x + 24 - 4x = 30
2x = 6
x = 3
So it should be opened after 3 hours i.e. 12:30 am

Bunuel · Answer

Not sure how you got the numbers there. Combined rate is INFLOW of 1/5-1/15=2/15 pool/hour...

We are interested on time needed for outlet pipe to compensate the excess of 1/5 of the pool.

Temurkhon · Answer

Inlet: 1/5 t/h
Oulet: 1/15 t/h
together working 1/5-1/15=2/15 t/h

2/15*6=12/15 filled, so 3/15 unfilled

3/15:1/15=3 hours of outlet should subtract. 6-3=3 hours

Answer: D

PrakharGMAT · Answer

Hi  chetan2u ,

I am able to get the solution from the following method-
1/5 * t + 2/15 * (6-t) = 1 (Since the tank should be full after 6 hours) 
t/5 + 12/15 -2t/15 = 1 
12/15 + t/15 = 1 
t/15 = 3/15 
t=3

However, I want to discuss 1 more approach
Inlet pipe rate= 1/5
outlet pipe rate= 1/15
Combined rate of Inlet and Outlet = 1/5 - 1/15 = 2/15

As, mentioned in the question the tank gets filled in 6 hours.
We can say that Inlet pipe works for 6 hours and
and Inlet = outlet pipe works for x hours

So, I tried to make the equation as

(1/5)*6 + (2/15)*x= What do I need to put on RHS

Can you please assist.

Thanks and Regards,
Prakhar

Nevernevergiveup · Answer

PrakharGMAT

when you say 2/15 it means the combined work of both inlet and outlet. then you cannot consider 1/5 work of inlet for 6 hours since it will overlap with the combined time.

then equation will  \frac{2}{15}x+\frac{1}{5}(6-x)=1 (Since the tank should be full after 68 hours)
solving this equation will result  x=3 .

mm229966 · Answer

Inlet pipe's rate it 1/5. If it works for 6h: 6* 1/5 = 6/5 work done; which is 1/5 more than needed. 
To pump out extra 1/5 water the outlet pipe needs 15 * 1/5 = 3 hours.
So if inlet starts at 9:30 and works for 6h., and outlet for 3h.: 9:30am + 6 hours - 3 hours = 12:30pm.

Answer: D.

Runjhun26 · Answer

Inlet takes 5 hours and outlet takes 15 hours, LCM= 15 = total capacity
which means inlet works at 3 units/hour and outlet 1 unit/hour.

In 6 hours, inlet will fill (6*3) 18 units which 3 more than desired capacity
and since outlet works at 1 unit/hour, it will take 3 hours to bring it down to 15.

required time= 3 hours from 9:30= 12:30

Vivek1707 · Answer

This question can be solved very quickly by making just one linear equation

The hours are given i.e 6 hours 
Let total work be 90 units

Inlet pipe inflow = 18 units per hour (90/5)
Outlet pipe outflow = 6 units per hour (90/15)

Since the inflow pipe will be running for the entire 6 hours, let y be the hours that the outflow pipe is running

18 * 6 - 6y = 90
y = 3 hours

Since outflow pipe needs to run for 3 hours
It means it needs to start at 12:30

A tank has both an inlet pipe and an outlet pipe. Working

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A tank has both an inlet pipe and an outlet pipe. Working

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