A cistern has a leak which empty it in 8 hrs, A tap is turned on which

Question

A cistern has a leak which empty it in 8 hrs, A tap is turned on which admits 6 liters a minute into the cistern, and it is now emptied in 12 hours, How many liters does the cistern hold ?

A. 8640
B. 8740
C. 8840
D. 8540
E. 8940

chetan2u · Accepted Answer

Yes, now the Q is complete..

Lets find 1-hour work-  
1-hr work of leakage = 1/8...
1-hr work of both combined = 1/12...
so 1-hour wk of tap = \frac{1}{8} - \frac{1}{12} = \frac{3-2}{24} = \frac{1}{24}.. 
 
so TAP will take 24 hr to fill the cistern..
speed of tap = 6 ltrs per minute = 6*60 = 360 ltrs per hour..

Capacity = 360*24 = 8640..

A

chetan2u · Answer

Hi,

But if you want to work on the method that you have applied..

the water filled up initially in tank is emptied in 8 hours but now it takes 12 hours to remove the water filled up initially and also the water being filled up by the tap..
so the water filled up by the tap is being removed in 4 hours,

as you have found the water filled up is 4320...
so leakage removes 4320 in 4 hours and therefore the capacity is WHAT it removes in 8 hours = 4320 *2 = 8640..

adiagr · Answer

Suppose the volume of cistern is V. 
Leak can be considered as a negative tap. The outflow through the leak is (V/8) Litres per hour.
Incoming water is: 6 Ltrs per minute = 6 *60 litres per hour = 360 Litres per hour

Total Volume that is emptied = V 
 
 \frac{V}{(  V/8} ) - 360   = 12 hours

V =  \frac{12 V}{8}  - 360 *12

\frac{4 V}{8}  = 360 *12

V = 360 * 12 * 2 = 8640 Litres

Alex75PAris · Answer

Incoming water = + 6 l/min = 360 l/h
Outcoming water = - X/8 l/h, X being the cistern's volume.

So, (360 - X/8)*12 = x
x=1728

Why is it false ?

chetan2u · Answer

hi,

it is false because the equation is not correct.....

which is more - INCOMING or OUTGOING? 
Outgoing as the cistern gets emptied when BOTH are switched on..

so equation is..
 ( \frac{X}{8}-360)*12 = x...............\frac{3x}{2}-4320 = x...........................\frac{x}{2}=4320..................x = 8640

hope it helps

Divyadisha · Answer

chetan2u , kindly suggest if below method is correct.

Inflow of water in 12hrs with rate 6 lit/min= 6*60*12= 4320

But, the same volume is emptied in 12 hrs, so the total capacity = total inflow + total outflow= 4320+4320= 8640

chetan2u · Answer

Hi,

May not be correct for two reasons-
1) This would mean the answer will remain same irrespective of the speed of leakage, but it is dependent on BOTH leakage and inflow..
2)
 
No the volume that is emptied in 12 hrs is INFLOW + CAPACITY.....

May be the answer has matched here because the time taken to fill up tank is found 24 hours, double of 12hours

Divyadisha · Answer

Thanks  chetan2u . I understood now.

Initial rate- Rate of inflow= Final rate

x/8- 360= x/12

gracie · Answer

if leak empties 1 cistern in 8 hours,
then it will empty 1 1/2 cisterns in 12 hours
but with tap running, it only empties 1
thus, tap fills 1/2 of cistern in 12 hours
12 hours*360 lph=4320 liters
4320/(1/2)=8640 liters
A

nbestman · Answer

Could you help me understand why you got 4320, but then divided by half?

Thanks!

AR15J · Answer

Hi nbestman

Initially, the question says that the leak can empty the cistern in 8 hours, but when the tap which fills the cistern at certain rate is opened, the cistern get empty in 12 hours. (That means leaking lts/hr are more than filling lt/hr)

If there would not be any tab to fill the cistern, the leak would have emptied 1 1/2(3/2) cisterns in 12 hours (as it empty 1 cistern in 8 hours)
but with the tab running, it only empties 1. that means tab must have filled 1/2 cistern in 12 hours.

If half cistern can be filled in 12 hours by the tab then full cistern will be filled in 24 hours by the tab

we have to find out the capacity of the cistern. As we know that, in one min, tab fills 6 lts; in 24 hours(24*60 mins), tab will fill 6*24*60= 8640 lts
 (Gracie calculated the capacity of half cistern first and multiplied it by 2).

If you find it difficult to approach the question in this way, here is another way--

Another approach : 
Let's say that the tab fills the cistern in x hours and we know that leak empty the cistern in 8 hours. We also know when both are open, it get empty in 12 hours

1/8-1/x=1/12 (why not 1/x -1/8=1/12 because cistern get empty )
x=24
we have to find out the capacity of the cistern. As we know that, in one min, tab fills 6 lts; in 24 hours(24*60 mins), tab will fill 6*24*60= 8640 lts

Hope it helps..

RMD007 · Answer

Simple work rate approach:

Let the total capacity be x.

Rate of leak - x/8 
Rate after opening tap - x/8 - 360 --> 1min - 6litres so 1hour -- 360ltrs.

x = ((x/8) - 360)*12;

x= 8640

georgekaterji · Answer

let x be the rate of leakage, and V be the volume of the cistern

In first case (tap not turned on):   x=v/8  liters/hour

=> 8*x=v

In second case (tap turned on) : (x-360)= V/12  liters/hour

=> 12*(x-360)=v

Now, equating V:

12x - 4320=8x
4x=4320
x=1080

=> v= 8*x=8*1080=8640 Liters

Hope this helps

JeffTargetTestPrep · Answer

We can let x = the number of liters the cistern holds. Thus, the rate of the leak (outflow) is x/8 liters per hour. The rate of the tap (inflow) is 6(60) = 360 liters per hour. The net rate is the difference between the outflow and inflow, which is given as being equal to a net outflow of x/12 liters per hour. We can create the following equation:

x/8 - 360 = x/12

Multiplying both sides by 24, we have:

3x - 8640 = 2x

x = 8640
 
Answer: A

gracie · Answer

with tap running, leak empties cistern 12/8=1 1/2 times 
so tap fills 1/2 cistern in 12 hours
so cistern holds 12 hrs*60 min*6 liters*2=8640 liters
A

Karmesh · Answer

I think all the explanations above capture the different ways of approaching the question beautifully.
I would just like to share an approach which is really  helpful during a time crunch or when you can't figure out how to solve.

Cistern empties tank in 8hrs. 
The capacity of tank = 8*time taken by cistern.
Hence, the answer must be a multiple of 8. 
ONLY option A complies.

Always write down what the question tells you and then pause and think before digging in. A 10 sec pause might just save you a whole lot of trouble.

krishna_sunder_ · Answer

RATE(L/h)          *              TIME                   = WORK

inlet                       360
outlet                    -T/8                                  8                      = -T (total volume)

inlet+outlet         360-(T/8)                           12                      = -T

solving the equation   * 12 = -T
we get T = 8640

saynchalk · Answer

I looked for the option that was divisible by 3 and 2 since provided numbers are mainly factors of 3 & 2 and got the right answer

DhanyaAbhirami · Answer

> LCM(8,12) = 24
> Drain rate : -3 unit/h
> Drain + Tap rate : -2 units/h
> Tap rate = 1 units/h
> Tap takes 24 hours to fill tank
> Tap filles 6L/min = 6 X 60 X 24 = 8640 L

A cistern has a leak which empty it in 8 hrs, A tap is turned on which

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A cistern has a leak which empty it in 8 hrs, A tap is turned on which

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