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TheNightKing
Two pipes A and B can fill a tank in 24 minutes and 32 minutes respectively. If both the pipes are opened simultaneously, after how much time should B be closed so that the tank is
full in 18 minutes?
(a) 6
(b) 8
(c) 10
(d) 11
(e) 13

A's 1 min work = 1/24
B's 1 min work = 1/32

Let B is closed after T min

i.e. A works for 18 minutes and B works for only T mins and work is done completely

18*(1/24) + T*(1/32) = 1
T*(1/32) = 1/4

T = 8

Answer: Option B
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\((\frac{x}{24}+\frac{x}{32})t + (\frac{x}{24})(18-t)=x\) where \(x\) is the total capacity and \(t\) is the duration for which the two pipes work together

\(\frac{t}{24}+\frac{t}{32}+\frac{3}{4}-\frac{t}{24}=1\)

\(\frac{t}{32}=1-\frac{3}{4}=\frac{1}{4}\)

\(t=\frac{32}{4}=8 hours\)

Answer is (B)

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