Latest Elitmus Aptitude Question SOLUTION: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to

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(#M40164643) ELITMUS Numerical Ability question Keep an EYE

A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 litres a minute. When the tank is full, the inlet is opened and due to the leak the tank is empty in 8 hours. The capacity of the tank (in litres) is

Asked In Elitmus Sniper (7 years ago)

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Devendra Marghade  (7 years ago)

5760 litres

Let capacity of the tank be x litres.
Inlet pipe can fill 4*60=240 litres in 1 hr.
Leakage per hour = x/6 litres.
Given when tank is full and inlet is opened, tank is empty in 8 hrs.
=> Quantity (Full tank + Filling in 8 hrs) = Quantity (Leakage in 8 hrs)
=> x + 240*8 = 8*(x/6)
=> 6x + 11520 = 8x
=> x = 5760

Is this solution Helpfull? Yes (15) | No (1)  

Sayantani Maiti  (7 years ago)

Work done by the inlet in 1 hour = 1/6 − 1/8 = 1/24
Work done by inlet in 1 min= 1/24 ∗ 1/60 = 1/1440
Volume of 1/1440 part = 4 liters
Volume of whole = (1440 * 4) litres = 5760 litres.

Is this solution Helpfull? Yes (5) | No   

Harshit Gupta  (7 years ago)

when the tank is full and the inlet pipe is opened water is leaked out of the tank as,
1/4-1/6=1/24
therefore in every 1hour 24litres of water is leaked out.
the rate of water is 4litres a minute
therefore, capacity of tank is=24*60*4=5760litres

Is this solution Helpfull? Yes (3) | No   

swati jain  (7 years ago)

5760 litre is the correct answer

Is this solution Helpfull? Yes (1) | No   

kln  (6 years ago)

a part empty the tank =1//8-1/6=2/48=>1/24 inhour
in min( 24*60=1440)
inlet pipe fills 4 lit a min
capacity can hold the tank=4*1440=5760lit

Is this solution Helpfull? Yes (1) | No   

jitendra idpache  (7 years ago)

ans :1440 L

Is this solution Helpfull? Yes | No (3)  

aditya sarode  (7 years ago)

ans is 4320 litrs

let the discharge capacity of the tank be L/360 lit per min

also the filling capacity of the tank be given as 4 lit per min

after 6 hrs due to filling the tank cant get emptied then water in the tank = 4*(6*60min)= 1440 lit

also after 2 hrs the tank is filled = 4*(2*60)=480 lit

then water in tank after 8hrs =1440+480=1920 lit

if only discharge tap is opened then the tank empties in 6 hrs

if both filling and discharge happens simultaneously then this 1920 lit get emptied in 2 hrs to make tank fully empty

hence cumulative discharge capacity = 1920/(2*60) = 16 lit/min

above capacity is cumulative i.e considering filling and discharge at the same time (as in relative velocity
approach)

actual discharge = 16-4 = 12 lit/min

hence tank capacity = 12 lit/min * 360min = 4320 litre

Is this solution Helpfull? Yes | No (6)  

harshit yadav  (6 years ago)

time taken to fill the tank by inlet=-(1/8)+(1/6)
total volume=4/(1/60)*24=5760

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babaji  (6 years ago)

outlet can empty it in 6 hrs;
inlet can fill 240 lts in 1 hr:
when the inlet and oulet both are open then it is taking 8 hrs(when the tank is already full);
let x be the full tank capacity ?
x+(240*8)=this ltrs of water is finishes by 8 hours.(we know that it can empty in 6 hours so now we ll find for 8 hrs)=
(x/6)*8+=x+(240*8)=ans

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Rohan Bhatnagar  (5 years ago)

let L be the leak and I be inlet
suppose capacity be 24
now L->-6 hours hence efficiency will be -4l
4l/min =240l/hour
then efficiency after inlet is open =24/-8=-3l(both are open at present)
efficiency of inlet will be -3+4=1l/hour
this 1 l corresponds to 240l /hour thus -3l will make 720l/hour
as tank is completely empty in 8 hours so in 8 hours 8*720 =5760l
note :negative sign is for emptying.

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Sankalp Verma  (5 years ago)

A-Inlet
B-leakage

take there 1hr efficiency so,
A- 4*60=240L
B- x/6 ( x is the capacity of tank in Ltrs)
Now as given
it takes 8 hours to empty the tank when both of them are opened so,

X/(X/6 - 240) = 8
X= 5760ltrs

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