Aptitude - Pipes and Cistern - Discussion

L.C.M of 20, 15, 24 = 120 unit total capacity.

120/3 = 40.
40 * 3 = 120.

Why making the values in the ratio one we get.

C = 1/15 - (1/20 + 1/24).

Given,

First pipe takes 20h.
Second pipe take 24h.

ALL together take 15h.

Assuming that capacity of tank L. C. M [20, 24, 15] = 120.

First pipe can fill 6u/m.
Second pipe fill 5u/m.

All three fill 8u/m -------> 1.

First and second together fill in 11m/u----------> 2.

From 1 and 2 we get;

Third pipe fills the tank in 3u/m that is 120/3 = 40u of total fill.

But given 3 gallons are empty.

3 * 40 = 120gallons (capacity of tank).

120 gallon is waste water, which drains out from the tank in 15 min.

Let, the capacity of the tank is x gallon.

3 pipes 1 min can fill up (1 / 20 +1 / 24 - 3),

So, 15 min can fill up, 15 (1 / 20 + 1 / 24 - 3),

We get 15 (1 / 20 + 1 / 24 - 3) equally to x.

We get the calculation of x is 120 gallons.

How can we solve this problem by the unitary method?

Let the capacity of the tank or pump X gallons.
The first pipe can fill the tank in 20 min.
The second pipe can fill the tank in 24 min.
1st pipe 20 min. fill X gallon. So, First pipe in one min can fill X/20 gallons.
So, the second pipe can fill in X/24 gallons.
And the third pipe flows out 3 gallons per minute.
So, X/20 + X/24 - 3 equal X/15 therefore X equal 120 gallons.

The part of tank filled in 1 min by all pipes=(1/20)+(1/24)-(1/x).
= (44x-480)/480x.

The time required to fill 1 tank.
= 480x/(44x-480) minutes.

Where, x = time in minutes required to empty the tank by the waste pipe.
But all pipes fill the total tank in 15 minutes.

So, 15 = 480x/(44x-480).
x = 40 minutes.

The capacity of tank = discharge per minute * time.
= 3 * 40,
= 120 gallons.

I have the best solution here.
take LCM of 20,24 = 120

Pipe c can empty 3 gallon/minute.
120/3 = 40 minute.
-----------------------------|
minute | efficiency |
-------------|---------------|
a = 20 | 6 |
b = 24 | 5 |
c = 40 | 3 |
******************************
(a+b-c) --> 11-3 = (+8)

120/8 = 15 minute.

120-gallon tank will fill in 15 minutes,
A can fill in 24 minutes or 5 gallons/minute,
B can fill in 20 minutes or 6 gallons/minute.

C can empty in 40 minutes or 3 gallons/minute <---question says.

Your logic is most acceptable or easy to me, Thanks @Rabi.