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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