Q. 573.7( 20 Votes )

Two water taps together can fill a tank in 6 hours. The tap of larger diameter takes 9 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Answer :

Let the time taken by tap of smaller diameter to fill the tank be x hours

The time taken by tap of larger diameter to fill the tank = x – 9 hours


Let the volume of the tank be V


Volume of tank filled by tap of smaller diameter in x hours = V


⇒ Volume of tank filled by tap of smaller diameter in 1 hour = V/x


⇒ Volume of tank filled by tap of smaller diameter in 6 hours =


Similarly, Volume of tank filled by tap of larger diameter in 6 hours =


Volume of tank filled by tap of smaller diameter in 6 hours + Volume of tank filled by tap of larger diameter in 6 hours = V



⇒ 


⇒ 


⇒ 


⇒ 12x – 54 = x2 – 9x


⇒ x2 – 21x + 54 = 0

⇒ x2 – 18x – 3x + 54 = 0

⇒ x(x – 18) – 3(x – 18) = 0

⇒ (x – 18)(x – 3) = 0
⇒ (x – 18) = 0 and  (x – 3) = 0

⇒ x = 18 or x = 3


For x = 3,  time taken by tap of larger diameter is negative which is not possible

Thus,  x = 18


Hence the time taken by tap of smaller diameter to fill the tank be 18 hours

The time taken by tap of larger diameter to fill the tank = 18 – 9 = 9hours

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