Question

Two pipes running together can fill a tank in 100\9 minutes, if one pipe takes 5 minutes more than other to fill the tank find the time in which each pipe would fill the tank.

Answer 1

Let one of the pipe take x minutes to then the slower pipe will take (x+5) minutes.

Time taken by both pipe to fill the tank = 100/9 minutes

Portion of tank filled by faster pipe in 1 minute = 1/x

Portion of tank filled by faster pipe in 1 minute = 1/(x+5)

Portion of tank filled by both pipe in one 1 minute = 1/(100/9) = 9/100

A/q,

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 and x = 20

But x can't be negative as it represents time.

Therefor, X = 20 minutes.

Time taken by faster pipe to fill the tank = 20 minutes.

Time taken by slowerr pipe to fill the tank = 20+5 = 25 minutes.