Aptitude - Pipes and Cistern - Discussion

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.

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.

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.

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.

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.

How 7/3 becomes 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.

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

Through LCM method:

Pump A fills in = 2hrs.
Leaking pump = 7/3 hrs.

Take LCM of 2 and 3 = 6 units,
Therefore,
Pump A = 3 u/h,
Leaking pump = 14 u/h,

Hence, the leaking pump can drain all the water in = 14 hours.

Pipe A could fill an empty cistern in 18 hours while Pipe B can drain a filled cistern in 30 hours. When the cistern is empty, Pipe A is turned on for an hour and then turned off. Now Pipe B is allowed to drain out water from the cistern for an hour and then turned off. The pipes were alternately left open for an hour each time till the cistern was full. How much time did it take for the cistern to be full?

Can anyone help me to solve this?