Two inlets pipes can individually fill a cistern in 10 minutes and 20

Question

Two inlets pipes can individually fill a cistern in 10 minutes and 20 minutes respectively. However it took them 8 minutes to fill the cistern working simultaneously, because of a leak at the bottom of the cistern. In how many minutes would the leak empty the entire filled cistern if the inlet pipes are closed?

A. 40 minutes
B. 42 minutes
C. 46 minutes
D. 48 minutes
E. 50 minutes

A. 40 minutes
B. 42 minutes
C. 46 minutes
D. 48 minutes
E. 50 minutes

Abhishek009 · Answer

Let the capacity of the tank be 40 units

So, Efficiency of the 2 inlets pipes are respectively 4 units/min & 2 Units/min

Thus, Combined efficiency of the 2 inlet pipes are 6 units/min

Now, let the efficiency of the outlet pipe be e

So, We have (6 - e )*8 = 40

Or, 6 - e = 5

Or, e = 1

Now Time required to empty the cistern will be 40/1 = 40 , Answer must be (A)

Jawad001 · Answer

Let the time of leak be x minutes.
(1/10 + 1/20 – 1/x)*8 = 1
(1/10 + 1/20 – 1/x) = 1/8
1/x = (1/10 + 1/20 -1/8)
1/x = (4+ 2-5)/40
X = 40(Minutes)

Lakshyamanchester · Answer

A is the correct option.
1/x+1/y-1/z=1/10+1/20-1/8
1/x+1/y-1/z=-1/40
 =40 minutes to empty

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KarishmaB · Answer

The rates of the inlet pipes are 1/10 and 1/20. Combined rate = 1/10 + 1/20 = 3/20
However, because of the leak, it took them 8 mins to fill 
i.e. Combined rate of inlets - Rate of leak = 3/20 - Rate of leak = 1/8
Rate of leak = 1/40

So it will take the leak 40 mins to empty out the entire filled cistern if inlet pipes are closed.

Answer (A)

Pradd1984 · Answer

Let's say the cistern can hold 20L:

Pipe one takes 10 minutes: 2L/minute

Pipe 2 takes 20 minutes: 1L/minute

together the pipes: 3L/minute

Due to the leak it took 8 minutes with both pipes working together. Without a leak the pipes could normally fill 24L in 8 minutes. (8min X 3L per min)
This means the pipe lead 4L in 8 mins (24-20) or 1/2 L every minute (8/4).

Therefore to leak the entire 20L it would take 40 minutes: (20 / 1/2).

Answer: A

CrackverbalGMAT · Answer

Two inlets pipes can individually fill a cistern in 10 minutes and 20 minutes respectively. However it took them 8 minutes to fill the cistern working simultaneously, because of a leak at the bottom of the cistern. In how many minutes would the leak empty the entire filled cistern if the inlet pipes are closed?

A. 40 minutes
B. 42 minutes
C. 46 minutes
D. 48 minutes
E. 50 minutes

Let's use LCM method to solve this Time & Work question.

Assume that volume of the cistern = LCM (10,20 ,8) = 40 L

Calculating Per min work each pipes:

Amount of water filled by inlet pipe A per min = 40/10 = 4 L/ min
Amount of water filled by inlet pipe B per min = 40/20 = 2 L/ min
Amount of water filled by 2 inlet pipes, along with leak = 40/8 = 5 L/ min

i.e 4 + 2 - Leak/min = 5 
Leak/min = 1 L

So, the leak will take 40 mins to empty the entire filled cistern, if the inlets pipes are closed.

Option A

Thanks,
  Clifin J Francis,
GMAT SME

Two inlets pipes can individually fill a cistern in 10 minutes and 20

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Two inlets pipes can individually fill a cistern in 10 minutes and 20

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