Question 72
Two taps P and Q can fill a cistern in 30 and 20 minutes respectively. Both P and Q were opened for a few minutes after which P was closed. The rest of the cistern was filled by Q in 5 minutes. After how many minutes was pipe P closed?
Solution
$$ work done = efficiency \times time $$
work done = LCM( 30,20)
= 60
efficiency of pipe P = $$ \frac{60}{30} = 2 $$
efficiency of pipe Q = $$ \frac{60}{20} = 3 $$
according to question
$$ ( efficiency of P + efficiency of Q)x + efficiency of Q \times 5 = 60 $$
where x = time
$$ (2 + 3)x + 3 \times 5 = 60 $$
solving x = 9
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