Q28 of 47 Page 1

To fill a swimming pool two pipes are to be used. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, only half 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.

Let the bigger pipe fill the tank in x hrs.


∴ the smaller pipe fills the tank in (x + 10) hrs.


Given that the bigger pipe is used for 4hrs and smaller pipe for 9hrs and together they fill half the tank.


So,



⇒


⇒ 2(13x + 40)=x(x + 10)


⇒ 26x + 80=x2 + 10x


⇒ x2-16x-80=0


⇒ x2-20x + 4x-80=0


⇒ x(x-20) + 4(x-20)=0


⇒ (x + 4)(x-20)=0


⇒ x=20 or x=-4(rejected)


Therefore, The time taken by larger pipe=20hrs.


And time taken by smaller pipe=20 + 10=30hrs


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