A cistern which has leak in the bottom is filled in 15 hours. Had there been no leak, it could have

M4maths Previous Puzzles

28 Jul 2015 Time and work

A cistern which has leak in the bottom is filled in 15 hours. Had there been no leak, it could have been filled in 12 hours. If the cistern is full, the leak can empty it is

OPtion

1) 3 hours
2) 6 hours
3) 10 hours
4) 12 hours
5) 14 hours
6) 15 hours
7) 28 hours
8) 30 hours
9) 24 hours
10)60 hours

Solution

Work done by the leak in 1 hours = (1/12 - 1/15) = 1/60
Therefore lean can empty the full cistern in 60 hours.

Option 10)

Correct Option: 10 Best Solution (29)

Kethineni Vinodh   9 years AGO

1/12+1/leak=1/15
1/leak=1/15-1/12
1/leak=-1/60
minus indicates leak i.,e 60 hours

Like? Yes (11) | No   

neha gupta   9 years AGO

Let the pipe which fills the cistern fills it in x hours , so its one hour work is 1/x
and the leak which empties it empties it in y hours , so its one hour work is 1/y
according to ques
1/x - 1/y = 1/15
and
1/x = 1/12
so x=12
1/12 - 1/15 = 1/y
on solving it we get
y = 60
thus its answer is 60 hours

Like? Yes (10) | No (1)  

Abhishek Mohanty   9 years AGO

let B be the reason to fill the cistern without any leak then work done by B in hour =(1/12).

similarly let A can empty the cistern in x hours without B filling simultaneously.then work done by B in 1 hour=(1/x).

Net work work done in 1 hour simultaneously by A & B =(1/12)-(1/x)=(x-12)/12x.
so total time to fill the cistern=[12x/(x-12)]=15 hours (given).

Solving we get x=60.

Like? Yes (5) | No   

Devendra Marghade   9 years AGO

If leakage can empty the full tank in 'x' hours, then
(1/12)-(1/x)=1/15
On solving, x=60
Option (10)

Like? Yes (4) | No   

UJJWAL KANT   9 years AGO

cistern with leak will fill 1/15 of cistern in an hour
cistern without leak will fill 1/12of cistern in an hour
hence to completely empty the tank 1/12-1/15=1/60
i.e 60 hours

Like? Yes (5) | No (1)  

Piyush Telang   9 years AGO

Let 'F' be the hours in which the cistern can be completely filled without any hole in it & 'E' be the hours in which the hole can empty the cistern when it is completely filled.
Such that : In 1 hour, one-Fth part of the cistern is filled and one-Eth part of the cistern is emptied respectively.
Then 1/F - 1/E = 1/15;
which means in 1 hour one-fifteenth of the cistern is filled having a hole.
And 1/F = 1/12;
which means in 1 hour one-twelfth of the cistern is filled without a hole.
1/12 - 1/E = 1/15
=> 1/E = 1/12-1/15 = 1/60
=> E = 60 hours.
Thus the leak can empty the full cistern in 60 hours.

Like? Yes (5) | No (2)  

Rahul kumar   9 years AGO

let x be time taken by leak to empty full tank
1/12-1/15=1/x
x=60hrs

Like? Yes (4) | No (1)  

pankaj chaurasia   9 years AGO

tank can be fill full in (without leak)=12 hour
tank can be fill full in(with leak)=15 hour
now,
tank filled in 1 hour=1/12
tank fill in 1 hour with leak=1/15
therefore,,,,3 hour is taken extra when there is been a leak in tak,,
so tank can be emptied in
1/12 - 1/15=1/60
now , do 1/60 time will be used to empty the tank in 1 hour therefore
total time is reciprocal of 1/60= 60 hour

Like? Yes (3) | No   

Kshitiz Khandelwal   9 years AGO

filling rate x l/hr
leak rate y l/hr
ATQ
15(x-y)=12x
on solving
x=5y
which gives
leak will empty it in 60 hours

Like? Yes (3) | No (1)  

praveendas   9 years AGO

leaked water from the tank in one hour is (1/12-1/15)=1/60
in order to make it full empty time required is 60 hours

Like? Yes (2) | No (1)  

shivani gupta   9 years AGO

1/x-1/y=1/15
1/12-1/y=1/15
1/12-1/15=1/y
1/60=1/y
y=60 hrs

Like? Yes (1) | No   

Ria Chandra   9 years AGO

consider the time taken by the pipe to fill the tank as p and time with which tank gets empty as e.
so 1/p-1/e=1/15(given)
since, 1/p=1/12
so 1/e=1/60
hence, answer is 60 hours

Like? Yes (1) | No   

SUNIDHI   9 years AGO

in one hour the leak empties 1/60th part of the tank in 60 hrs it will empty the tank

Like? Yes (1) | No   

Dinesh kumar   9 years AGO

(1/12)-(1/x)=1/15
(1/12)-(1/15)=1/x
1/60=1/x
X=60

Like? Yes (2) | No (1)  

Narendra Gopi   9 years AGO

1/x-1/y=1/15
-1/y=1/15-1/12
1/y=1/60
y=60hrs

Like? Yes (1) | No   

Vivek   9 years AGO

The time it takes to fill the cistern =12 hrs
The total time taken by the cistern and the leak =15 hrs
Therefore the time taken by cistern alone x
1/x = 1/12 -1/15
=1/60
x = 60 hrs
Hence the option is 10)

Like? Yes (1) | No   

anand vijay   9 years AGO

1 hour work if there is no leak in the tank= 1/12
1 hour work if there is a leak in the tank=1/15
so,time taken by the leak to empty the tank in 1 hour=1/12-1/15
1/60
total time to empty the tank=60 hour
option 10)

Like? Yes (1) | No   

Manish Dwivedi   9 years AGO

let the volume of cistern be v
so v ltrs can be filled in 12 hrs
so in 1 hr v/12 ltrs can be filled
so in 15 hrs total volume filled=15*v/12=1.25v
so in 15 hrs 0.25v volume is leaked
so total time to empty the cistern is 60hrs

Like? Yes (1) | No   

Subhash Gupta   9 years AGO

let required hours=h
then
1/12-1/h=1/15
h=60

Like? Yes (1) | No   

Haripriya   9 years AGO

1/12-1/15
(4-5)/60
1/60
so 60

Like? Yes (1) | No   

Soma Naresh   9 years AGO

let us assume that the work done by leaked pipe and other be x and y.
given work done by both is 15 hours
x+y=1/15
cistern filled by other pipe without having leak at 12 hours
y=1/152
then
x=(1/15)-(1/12)
x=-1/60
means x takes 60 hours to empty tank

Like? Yes (1) | No   

Altaf Hussain   9 years AGO

Let the capacity be 60. Rate at which it is filled with leak is 60/15=4 and rate at which it is filled Without leak is 60/12=5. Rate of leak is 1. It takes 60 hours.

Like? Yes (1) | No   

sonu kumar suman   9 years AGO

because in one hour it fill 1/12 if there had no leak.and if leak then it fill 1/15 in one hour.so,leak in one hour is 1/12 - 1/15=1/60.so for total time to empty full cistern is 60.

Like? Yes (1) | No   

Sushmita Ghanty   9 years AGO

part of the cistern emptied by the leak in 1 hr = 1/12 - 1/15 = 1/60
hence the leak will empty the cistern in 60 hrs

Like? Yes (1) | No   

VIKASH RAY   9 years AGO

when there is no leak the tank filled in 12 hrs.
so,in 1 hrs. the part of the tank filled is=1/12
let, due to the leak the tank can be empty in x hrs.
so, the part of the tank empty in 1 hrs. is=1/x
so,
(1/12)-(1/x)=(1/15)
on solving this we get x=60
so the tank can be empty in 60 hrs.

Like? Yes (1) | No   

GAUTAM CHAURASIA   9 years AGO

tank filling time with leak and without leak is 12 hour and 15 hour respectively.
now, talk about 1 hour,
tank filling time with leak and without leak is 1/12 hour and 1/15 hour respectively.
so,,,due to leak total extra time consumed in tank filling process in one hour is[ (1/12) - (1/15)= (1/60) ]

hence total time will be sufficient for empty the leak is 60 hours(reserve of 1/60)

Like? Yes (1) | No   

Subham Mahanta   9 years AGO

work done by the leak in 1 hour = (1/12 - 1/15) = 1/60
so, if the cistern is full, the leak can empty it in 60 hours
ans. is option (10)

Like? Yes (1) | No   

ANUSHKA   9 years AGO

Let The time taken to empty be x hrs.

so, 1/12-1/x = 1/15
1/x = 1/12 - 1/15
1/x = 1/60

Therefore, time taken to empty is 60 hours.

Like? Yes (1) | No   

aman aditya   9 years AGO

let cistern capacity is 12 liter
so if it took 15 hr with leakage which means it had 15 liter if water.
so it leaked 3 liter of water in 15hr.
so total water is 12 liter so it will take 60 hr

Like? Yes (1) | No (1)