Answer :

Time taken by both pipes to fill the tank

Work done by both pipes in a minute = 9/100

Let the time taken by one pipe to fill tank = x minutes

Work done by first pipe in one minute = 1/x

Time taken by another pipe to fill tank = x + 5 minutes

Work done by second pipe in one minute = 1/x + 5

work done by both pipes in one minute =

So,

200x + 500 = 9x^{2} + 45x

9x^{2} - 155x - 500 = 0

9x^{2} - 180x + 25x - 500 = 0

9x(x - 20) + 25(x - 20) = 0

(9x + 25)(x - 20) = 0

x = 20 or x = - 25/9(not possible as time is not negative)

time taken by first tank = 20 minutes and second tank is 25 minutes.

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