Filling An Empty Cistern

Since pipe A, B and C take 20, 15 and 12 minutes to fill a cistern, they fill 1/20, 1/15 and 1/12 of the cistern individually in one minute. Together they will fill 1/5 of the cistern in one minute. So it will take 5 minutes

Ra=1/20, Rb=1/15, Rc=1/12 Where R's is the rate of filling cistern by the pipes solve Ra+Rb+Rc=1/5 So, 5 mins

let us assume the capacity of cistern as 60 liters, the lcm of 20, 15 and 12... then the inlet of A, B and C becomes 3, 4 and 5 liters/minutes.... if all three are operated simultaneously, the inlet will be 3+4+5 = 12 liters per minute... then the time for filling the cistern will be 60 divided by 12 becomes 5 minutes

The pipes A,B and C alone can fill the cistern in 20,15 and 12 minutes respectively.

So, in 1 min, pipe A can fill $\frac{1}{20}$ part of the cistern, pipe B can fill $\frac{1}{15}$ part of the cistern and pipe C can fill $\frac{1}{12}$ part of the cistern if they work alone.

If all the three pipes are kept on, then in 1 min, they can fill $=\frac{1}{20}+\frac{1}{15}+\frac{1}{12}= \frac{6+8+10}{120} = \frac{24}{120} = \frac{1}{5}$ part of the cistern.

Then the pipes can fill the whole cistern in = $\frac{1}{\frac{1}{5}} = \boxed{5\text{min}}$

Pipe A takes 20 minutes to fill 1 cistern. Therefore pipe A will fill 1/20 parts of cistern in 1 minute. Similarly, Pipe B will fill 1/15 parts per minute and Pipe C will fill 1/12 parts per minute. If these three pipes work together then, In 1 minute they would fill 1/20 + 1/15 + 1/12 and therefore, 1/5 parts will be filled by all the three pipes in 1 minute. So, 1 fill cistern would be filled in 5 minutes.

Let x be the time it takes using three pipes to fill the cistern. And A=20mins, B=15mins, C=12mins. Then using the rate equation, 1 work per unit of time = the sum of individual works per unit time (1/x) = (1/A) + (1/B) + (1/C) (1/x) = (1/20) + (1/15) + (1/12) (1/x) = (3/60) + (4/60) + (5/60) (1/x) = 12/60 x = 5

A------> 20 min B------> 15 min c------> 12 min ,

A------> x (in diameter) B------> (20/15) x = 4/3 x C------> 20/12 x = 5/3 x the sum of all diameters is (x + (4/3)x + (5/3)x) = 4 x then the sum of all diameters is 4 times the diameter of pipe A so if A takes 20 min so all of them together would take 5 min ( 20/4)