Aptitude - Pipes and Cistern - Discussion

A = 20 min,
B = 24 min,
Let, C = x min.

Then, capacity = lcm of A,B,C =120x.
So, efficiency of A = capacity / time taken by A,
= 120x/20.
= (+) 6x [since it's used for filling].

Similarly, efficiency of B = 120x /24 = (+) 5x,
Efficiency of C = 120x / x = (-) 120. [since it's used for emptying]
Therefore, total efficiency = 6x + 5x -120.

So, time = (capasity / total efficiency) unit.
= (120x / (6x + 5x -120)) min.

Now, (120x / (6x + 5x - 120)) = 15.
Or, 24 / (11x - 120) = 3,
Or, 33x - 360 = 24,
Or, 9x = 360,
Or, x = 40.

Therefore, capacity = lcm of 20, 24 and 40,
= 120.

So, the capacity of the tank is 120 gallon.

Two pipes can fill a tank in 20 and 24 minutes respectively and part filled by them is(1/20+1/24)

1gallon=~4litres

All the three pipes working together total tank fills in 15min
so 1part fills in 15min


waste pipe can empty 3 gallons per minute so the volume of tank emptying by waste pipe is total filled tank minus part filled by to pipes i.e 1/15-(1/20+1/24) x 1min= -1/40

that means in 1min waste pipe is emptying 1/40part of total tank

given ,
waste pipe can empty 3 gallons per minute

therefore total volume is 1/40=3 gallons=>120 gallons

hence capacity of tank is 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.

A = 20 minutes.
B = 24 minutes.
C = 3 gallons per minute.

*The statement states that all three pipes working together can fill the tank in 15 minutes.

Therefore we can express it as : A+B+C = 15 minutes.

Say A+B+C=X.
Then C = X- (A+B).
Hence C = 15 minutes - (A+B).

Making the values in the ratio one we get.

C = 1/15- (1/20 + 1/24).
= 1/15 - 11/120.
= - 3/120.
= -1/40.

Thus the part filled by pipe C = 40 minutes.

For the volume of tank:

Given:

Pipe C = 3 gallons per minute.

Which means, in 1 minute = 3 gallons.

Then in 40 minutes = x.

x = 40*3 = 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.

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).

Pipe 1 can fill the tank in 20 minute and pipe 2 can fill it in 24 min.
Assume capacity of Tank is 120 gallons (LCM of 20,24).

Now,
Rate of pipe 1 = 120/20 = +6 gallons/minute.
Rate of pipe 2 = 120/24 = +5 gallons/minute.
Rate of drainage pipe = -3 gallons/minute (Note: -ve sign be because it is draining water).

Rate * time = Work.
(6+5+(-3)) * 15 min = 120 gallons.

@All.

We all know that lcm is the total capacity of the tank now here two values are already given which are 20 and 24 and 3rd value of the outlet pipe is not given so the logic here is the lcm of 20 24 and the unknown 3rd value will be divisible by all the three numbers right?

Hence check out all four options which option is completely divisible by 24 and 20 and that is your answer.

Let , the time taken by waste pipe to empty the tank is x.

Then part feed in one min.
(1/20+1/24) - 1/X = 1/15
11/120 -1/X = 1/15,
11X-120/120X = 1/15,
165X -1800= 120 X,
By solving we get x = 40 min.
So 40 min is the time which is taken by waste pipe to empty the entire tank

In problem it is given that waste pipe discharge 3 gallons per min.
40*3= 120 gallons is a capacity of tank.

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.