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.
⇒ 2(13x + 40)=x(x + 10)
⇒ 26x + 80=x2 + 10x
⇒ 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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