Aptitude - Pipes and Cistern - Discussion

Explain how come 2 1/3 = 3/7.

Let total units to be filled be 1 unit.

Then work done by the pump in 1h=1/2 now let x be the time taken by leakage to empty the tank i.e. 1 unit. The work done by leakage in one is 1/x units.

Now, as it takes 2 1/3 (or 7/3) to fill tank then work done in one hour with leakage will be =1/ (7/3) =3/7.

Therefore.

Work is done by pump without leakage per hour-work done by leakage in one-hour =work done by pumy with leakage.

i.e 1/2-1/x = 3/7.
i.e x = 14hours.

How 7/3 becomes 3/7?

Let v take two pipes A&B,

Let time of A=2hrs = 120months
Therefore the capacity of A(per mnt) = 1/120.

Now,

The time is taken by B=2 1/3 hrs = 140months.
Therefore the capacity of B(per mnt) = 1/140.

The difference between two pipes be the leakage capacity
i.e A-B = (1/120)-(1/140) = 1/840.

Therefore time was taken of leak = 840mnts = 14h.

A initially fills in 2 hrs.
Hence in one hr it fills 1/2 units,
With leak it takes 7/3 hrs,
Hence in one hr it fills 3/7 units (with leak).

(1/2)- leak per unit = 3/7,
Leak per unit = (1/2)-(3/7),
=1/14.

Per hr, it leaks units 1/14.
Total time taken to empty is 14 hrs.

The problem is exactly useful. But the tank when fulfill and quarter fill, there must be change the speed or press of water in the leak. So the water cannot throughout the same or regular behind to end.

X pipe can fill in tank.
Y tank filled with leak.
Time taken by leak to empty tank is (xy/y-x).
2*(7/3)/(7/3-2)=14.

Let take a leak as an outlet named B.

The capacity of the tank is 14/3 litr.e
A=7/3 litre/hr and,
B=-2.
A+B=-1/3.
Therefore.
14/3 / -1/3 = 14.

There is a simple formula.
a(1+(a/x)).
a= 2 hours.
x= 2 1/3- 2= 1/3.
Solution:
2(1+(2/ (1/3) )= 14.

Can anyone explain the answer in LCM method?