To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?

 To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?

 

 smaller pipe takes more time than bigger pitpe to fill the pool when used separately

let x hours be the time taken by bigger pipe alone to fill the pool

so given smaller pipe alone will take (x+10) hours to fill the pool

 

given that If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled

 

so [4/x] +[9/(x+10)] = 1/ 2

[4(x+10)+9x] / [x(x+10)] =1/ 2

 

[4x+40+9x] / [(x^2)+10x] =1/ 2

 

[13x+40] / [(x^2)+10x] =1/ 2

 

2[13x+40] =[(x^2)+10x]

26x +80= [(x^2)+10x] 

(x^2) +10x-26x-80=0

 

(x^2) -16x-80=0

 

splitting the middle terrm

(x-20)(x+4)=0

x =20 hours or x=-4(rejected)

x=20 hours

x+10 = 30hours

so

larger pipe alone will take 20 hours to fill the pool

while

smaller pipe alone will take 30  hours to fill the pool

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 questions in old cbse sample question papers for 10th  mathematics

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