Question

If cistern a can fill tank in 12 hours and cistern b can fill in 16 hours and c can empty tank in 8 hours then in how much time cistern can be full

Answer 1

Given, A can fill in = 12 hrs

B can fill in = 16 hrs

C can empty in = 8 hours

So, it will be full in = 1/12 + 1/16 - 1/8

= (4+3-6) / 48

= 1/48

So it will be full in 48 hours.

Answer 2

$in \: \: 1 \: hr \: \: a \: \: fills \: \frac{1}{12} th \: part \\ in \: \: 1 \: hr \: \: b \: \: fills \: \frac{1}{16} th \: part \\ in \: \: 1 \: hr \: \: c\: \: empties \: \frac{1}{8} th \: part \\ \\ when \: \: all \: \: operates \: \: together \: \: it \\ fills \: \: (\frac{1}{12} + \frac{1}{16} - \frac{1}{8} )th \: \: part \\ = \frac{1}{48}th \: part \: \: in \: 1 \: hr \\ \\ so \: \: it \: \: takes \: \: 48 \: hrs$