A cistern has two taps which fill it in 12 mi | vedclass

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Question

(B) Let the capacity of the cistern be the Least Common Multiple $(LCM)$ of $12, 15,$ and $20,$ which is $60$ units.
Efficiency of the first tap = $6

Vedclass · Accepted Answer

$10 	ext{ minutes}$

Vedclass · Answer

(B) Let the capacity of the cistern be the Least Common Multiple $(LCM)$ of $12, 15,$ and $20,$ which is $60$ units.
Efficiency of the first tap = $60 / 12 = 5$ units/min.
Efficiency of the second tap = $60 / 15 = 4$ units/min.
When all pipes are open, the net efficiency = $60 / 20 = 3$ units/min.
Let the efficiency of the waste pipe be $x$ units/min.
Then, $5 + 4 - x = 3$.
$9 - x = 3$, which gives $x = 6$ units/min.
Time taken by the waste pipe to empty the full cistern = $	ext{Total capacity} / 	ext{Efficiency of waste pipe} = 60 / 6 = 10$ minutes.

$A$ 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?

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