Question

two pipes p and q would fill an empty cistern in 24 minutes and 32 minutes respectively. both pipes being opened together, find when the first pipe must be turned off so that the empty cistern may be just filled in 16 minutes

Answer 1

it should turn of when the so that 32should become as 16 is of the 24"become a12 min ot will fillit in 16min

Answer 2

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.

Answer 3

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.