Question

To fill a cistern,pipe p q and r take 20, 15 and 12. the time in mins that 3 pipes fill in cistern is

Answer 1

Here it is given that pipe p can fill the cistern in 20 mins, pipe q in 15 mins and pipe r in 12 mins. To find out the actual capacity of the cistern, we need to take the LCM of all the three i.e 20,15 and 12 and we get the LCM as 60. Therefore​ the actual capacity of the cistern is 60(let's assume litres as the unit is not mentioned). Now, let's find out how much will each pipe fill the cistern in 1 min.
If in 20 mins pipe p can fill 60ltrs
Then in 1 min it can fill 60/20 ltrs=3ltrs
Similarly in 1 min pipe q can fill 60/15 ltrs=4 ltrs
And pipe r can fill 60/12ltrs= 5ltrs.

Therefore in 1 min the cistern will be filled by (p in 1 min)+(q in 1 min)+(r in 1 min)= (3+4+5)ltrs =12 ltrs

Now,
Time taken in fill 12 ltrs=1 min
Therefore,
Time taken to fill 60 ltrs=60/12(apply unitary method) =5 mins

Therefore, all the three pipes can fill the cistern together in 5 mins.