Question
Download Solution PDFPipes A and B can fill an empty tank in 10 hours and x hours, respectively. Pipe C alone can empty a full tank In 9 hours. When all three pipes are opened together, the tank is filled up completely in 18 hours. What is the value of x?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Pipes A and B can fill an empty tank in 10 hours and x hours, respectively. Pipe C alone can empty a full tank In 9 hours.
When all three pipes are opened together, the tank is filled up completely in 18 hours.
Concept used:
Total work = Efficiency (Work done per hour) × Total time taken
Calculation:
Let the capacity of the tank be 90x units.
Pipe A fills the tank by = 90x/10 = 9x units a hour
Pipe B fills the tank by = 90x/x = 90 units a hour
Pipe C empties the tank by = 90x/9 = 10x units a hour
According to the question,
(9x + 90 - 10x) × 18 = 90x
⇒ 90 - x = 5x
⇒ 6x = 90
⇒ x = 15
∴ The value of x is 15.
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