Question

Two tap a and b can fill a cistern in 16 min and 24 min respectively. How long after opening the both the taps, the tap b should be turned off so that the cistern may take 12 minutes to fill completely?

Answer 1

Cistern filled by tap A in 1 min. = 1/16
Cistern filled by tap B in 1 min. = 1/24

Now,
Let the time after which the tap B should turned off be t.

$( \frac{1}{16} + \frac{1}{24} )t + (\frac{1}{16} ) (12 - t)= 1 \\ \frac{5t}{48} + \frac{12 - t}{16} = 1 \\ \frac{5t + 36 - 3t}{48} = 1 \\ 2t + 36 = 48 \\ 2t = 12 \\ t = 6 \: mins.$

Tap B should be turned off after 6 minutes so that the cistern may take 12 minutes to fill completely.