An inlet pipe can fill an empty tank in 140 hours while an outlet pipe drains a completely-filled tank in 63 hours. If 8 inlet pipes and y outlet pipes are opened simultaneously, when the tank is empty, then the tank gets completely filled in 105 hours. Find the value of y.

Given:

Total inlet pipes = 8

Total time taken to fill the tank = 140 hours.

Drainpipe can empty tank = 63 hours 

Formula used:

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Calculations:

The total capacity of the tank is LCM of (63,140) = 1260

Efficiency of 8 inlet pipe = (1260/140) × 8

= 72 lit/h

Efficiency of y outlet pipe = (1260/63) × y

= 20y lit/h

Total time taken = (1260)/(72 - 20y) = 105

⇒ 1260 = 7560 - 2100y

⇒ 6300 =  2100y

⇒ y = 3

∴ The answer is 3.

Alternate Method 

⇒ Total Tank capacity = 1260 lit ( LCM of 140 and 63)

⇒ Efficiency of one inlet pipe = 1260 / 140 = 9 lit/h

⇒ Efficiency of 8 inlet pipe = 8 × 9 lit/h = 72 lit/h

⇒ Efficiency of one outlet pipe = 1260 / 63 = 20 lit/h

⇒ Efficiency of Y outlet pipe = Y × 20 lit/h = 20Y lit/h

According to question,

⇒ Efficiency of 8 inlet and Y outlet pipe = 1260 / 105 = 12 lit/h

⇒ 72 - 20Y = 12

⇒ 20Y = 60

⇒ Y = 3

∴ The answer is 3.