Answer :

Let the time taken by faster tap to fill tank is x hours,

⇒ In 1 hour, part of tank filled

⇒ In , part of tank filled

Therefore, time taken by slower tap is (x + 3) hours

⇒ In 1 hour, part of tank filled

⇒ In , part of tank filled

As, both taps fill the whole tank in hours.

We have,

⇒ 13x^{2} + 39x = 120 + 80xd

⇒ 13x^{2} - 41x - 120 = 0

⇒ 13x^{2} - 65x + 24x - 120 = 0

⇒ 13x(x - 5) + 24(x - 5) = 0

⇒ (13x + 24)(x - 5) = 0

⇒ or x = 5

But time can't be negative, therefore x = 5 hours

Time taken by faster tap = x = 5 hours

Time taken by slower tap = x + 3 = 8 hours.

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