Q79 of 82 Page 4

Two taps running together can fill a tank in hours. If one tap takes 3 hours more than the other to fill the tank, then how much time will each tap take to fill the tank? (CBSE 2017)

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,






⇒ 13x2 + 39x = 120 + 80xd


⇒ 13x2 - 41x - 120 = 0


⇒ 13x2 - 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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