Two pipes P1 and P2 can separately fill a cistern in 30 and 20 minutes respectively and a waste pipe P3 can carry off 11 litres per minute. If all the pipes are opened when the cistern is full,it is emptied in 42 hours. How many litres does the cistern hold?
131.4 litre
132 litre
130 litre
135 litre
Explanation:
Part filled by P1 in 1 minute =1/30
Suppose P3 can empty the cistern in x minutes. Then,
Part emptied by P3 in 1 minute =1/x
Net part emptied by all pipes together in 1 min
=$\dfrac{1}{42×60}=\dfrac{1}{2520}$
$\dfrac{1}{x}−\dfrac{1}{30}−\dfrac{1}{20}=\dfrac{1}{2520}$
⇒$\dfrac{1}{x}=\dfrac{211}{2520}$
⇒x=$\dfrac{2520}{211}$
i.e., P3 alone can empty the cistern in $\dfrac{2520}{211}$ minutes.
Capacity of the cistern =$\dfrac{2520}{211}$×11≈131.4 litre