Question
Download Solution PDFAn 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Total inlet pipes = 8
Total time taken to fill the tank = 140 hours.
Drainpipe can empty tank = 63 hours
Formula used:
If a pipe can fill a tank in x hours, part of it is filled in 1 hour =
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.
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