Question

35. Two pipes running together can fill a tank in 115 minutes. If one pipe takes 5 minutes
more than the other to fill the tank, find the time in which each pipe would fill the tank
separately.​

Answer 1

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Let the time taken by faster pipe be x minutes.
And the time taken by slower pipe be (x + 5) minutes.
Tank filled by faster pipe in 1 minute = 1/x
Tank filled by faster pipe in 1 minute = 1/(x + 5)
According to the Question,
⇒ 1/x + 1/(x + 5) = 9/100
⇒ (x + 5 + x)/x(x + 5) = 9/100
⇒ (2x + 5)/(x² + 5x) = 9/100
⇒ 200x + 500 = 9x² + 45x
⇒ 9x² + 45x - 200x - 500 = 0
⇒ 9x² - 155x - 500 = 0
⇒ 9x² - 180x + 25x - 500 = 0
⇒ 9x(x - 20) + 25(x - 20) = 0
⇒ (9x + 25) (x - 20) = 0
⇒ x = - 25/9, 20 (As x can't be negative)
⇒ x = 20 minutes.
Faster Pipe = x = 20 minutes
Slower Pipe = x + 5 = 20 + 5 = 25 minutes.