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After 12 minutes switch off P
See ,
Work done by Q in 16 minutes -1/32×16=1/2
That means P has to do 1/2 of the work left
Therefore Time taken by P,=24×1/2=12 minutes.
So after 12minutes P can be closed

Let volume of cistern be V Flow rate through pipe P is V/24 Flow rate through pipe Q is V/32 Flow rate through both pipes = V/32+V/24= 7V/96 let first pipe be turn off after x minute Cistern will be filled by 7V*x/96 volume Rest of volume be filled by pipe Q for 16-x minutes Volume filled by Q for 16-x minute is V*(16-x)/32 So we have 7Vx/96+ V(16-x)/32 = V ⇒ 7x/96 + (16-x)/32 = 1 ⇒ 7x +48 - 3x = 96 ⇒ 4x = 48 ⇒ x = 12 First pipe should be closed after 12 minutes.