P’s one minute’s work = 1/24
Q’s one minutes work = 1/32
Let the first pipe must turn off after x minutes
The cistern filled in 16 minutes
Then P’s x minutes work + Q’s 16 minutes work = 1
⇒ (1/24) × x + (1/32) × 16 = 1
x/24 + ½ = 1
⇒ x/24 = 1 – (½) = ½
⇒ x/24 = ½
⇒ x = 24/2 = 12
∴ After 12 minutes pipe P would turned off