Let the time taken by larger pipe alone to fill the tank= x hours
Therefore, the time taken by the smaller pipe = x+10 hours
Water filled by larger pipe running for 4 hours = 4/x litres
Water filled by smaller pipe running for 9 hours = 9/x+10 litres
We know that 4/x + 9/(x+10) = 1/2
Which on simplification gives:
x2−20x + 4x−80=0
x(x-20) + 4(x-20)= 0
(x +4)(x-20)= 0
x=- 4, 20
x cannot be negative.
Larger pipe would alone fill the tank in 20 hours and smaller pipe would fill the tank alone in 30 hours.