Question
Download Solution PDFOne of the two inlet pipes works twice as efficiently as the other. The two, working alongside a drain pipe that can empty a cistern all by itself in 8 hours, can fill the empty cistern in 8 hours. How many hours will the less efficient inlet pipe take to fill the empty cistern by itself?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
One of the two inlet pipes works twice as efficiently as the other.
The two, working alongside a drain pipe that can empty a cistern all by itself in 8 hours, can fill the empty cistern in 8 hours.
Concept used:
If two workers take X and Y hours respectively to complete a task independently, then time taken to complete the work together = \(\frac {XY}{X + Y}\) hours
Calculation:
Let the time taken by the more efficient inlet pipe be Q hours.
So, time taken by the less efficient inlet pipe = 2Q hours
According to the concept,
Time taken to fill the cistern if only two inlet pipes are open together
⇒ \(\frac {2Q \times Q}{2Q + Q}\) = \({\frac {2Q}{3}}\) hours
Time taken to fill the cistern if two inlet pipes are open together alongside the drain pipe
⇒ \(\frac {{\frac {2Q}{3}} \times {-8}}{{\frac {2Q}{3}} - 8}\) (A negative sign is taken since the drain pipe empties the cistern)
⇒ \(\frac {-16Q}{2Q - 24}\) hours
According to the question,
\(\frac {-16Q}{2Q - 24}\) = 8
⇒ \(\frac {-2Q}{2Q - 24}\) = 1
⇒ 2Q - 24 = -2Q
⇒ 4Q = 24
⇒ Q = 6
⇒ 2Q = 12
Now, time taken by the less efficient pipe to fill the cistern = 12 hours
∴ The less efficient inlet pipe takes 12 hours to fill the empty cistern by itself.
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