Question:

A cistern has two taps which fill it in 12 minutes and 15 minutes respectively. There is also a waste pipe in the cistern. When all the pipes are opened, the empty cistern is full in 20 minutes. How long will the waste pipe take to empty a full cistern?

Updated On: Oct 7, 2024
  • 12 minutes
  • 10 minutes
  • 8 minutes
  • 16 minutes
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The Correct Option is B

Solution and Explanation

Let the capacity of tank be 180 litres.
1st tap fills 180 litres in 15 minutes, 1min= 12 ltres fill
2nd tap fills 180 litres in 12 minutes, 1min= 15 ltres fill
3rd tap empties 180 litres in x minutes [let]... 1 min empty = \(\frac{180}{x}\) litres
Total filling time = 20 minutes
\(\Rightarrow\;\)\(20\times12 + 20\times15 - 20\times\frac{180}{x}\) = \(180\)
\(x = 10\) minutes

The correct option is (B): 10 minutes

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