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Question
Two pipes P and Q would fill an empty cistern in 24 minutes and 32 minutes respectively. Both the pipes being opened together, find when the first pipe must be turned off so that the empty cistern maybe just filled in 16 minutes.
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Solution
P's one minute's work =`1/24`
Q's one minute's work =`1/32`
Let the first pipe must turn off x minutes
The cistern filled in 16 minutes
Then P's x minutes work + Q's 16 minutes work = 1
`⇒1/24xx"x"+1/32xx16=1`
`"x"/24+1/2=1`
`⇒"x"/24=1-1/2=1/2`
`⇒"x"/24=1/2`
`⇒"x"=24/2=12`
∴ After 12 minute pipe P would turned off
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