Question

To fill a cistern, pipes $P,Q$ & $R$ take $20,15$ and $12$ minutes respectively. The time in minutes that the three pipes together will take to fill the cistern is

• A. $5$ min
• B. $10$ min
• C. $15$ min
• D. $15.66$ min

Answer 1

The correct option is A $5$ min

Given: pipes $P,Q,R$ takes $20,15,12$ minutes respectively to fill a cistern

To find the time in minutes that the three pipes together will take to fill the cistern

Sol: By taking the LCM of $12,15,20$ we will be able to find the actual capacity of the cistern, i.e., the actual capacity of cistern is 60 L(lets assume the unit to be litres)

IF pipe P can fill the cistern in $20$ minutes. Then in 1 min it can fill $\frac{60}{20}=3$ liters

Similarly in 1 min pipe Q can fill $\frac{60}{15}=4$ liters

And pipe R can fill $\frac{60}{12}=5$ liters

Therefore in 1 min the cistern will be filled by (P in 1 min)+(Q in 1 min)+(R in 1 min)= $(3+4+5)=12$ liters

Now,

Time taken to fill $12$ liters=$1$ minute

Therefore,

Time taken to fill $60$ litres=$\frac{60}{12}$ (apply unitary method) =$5$ mins

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