Q3 of 242 Page 9

Two water taps together can fill a tank in hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Let the smaller diameter tap fill the reservoir in ‘a’ hours


Larger diameter tap fills it in ‘a – 10’ hours.


Given, two water taps together can fill a tank in = 75/8 hours.


In 1 hour, part of tank filled = 8/75



⇒ 75(a + a – 10) = 8a2 – 80a


⇒ 150a – 750 = 8a2 – 80a


⇒ 8a2 – 230a + 750 = 0


⇒ 4a2 – 115a + 375 = 0


⇒ 4a2 – 100a – 15a + 375 = 0


⇒ 4a(a – 25) – 15(a – 25) = 0


⇒ (4a – 15)(a – 25) = 0


Value of a can’t be 15/4 as (a – 10) will be negative


Thus a = 25


Time taken by faster tap = 25 – 10 = 15 hours


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 2

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 4

Two pipes running together can fill a tank in minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.

 5

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