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?

• A. 12 minutes
• B. 10 minutes
• C. 8 minutes
• D. 16 minutes

Answer 1

Answer: (B)

10 minutes

Answer 2

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