Question

Two pipes x and y can fill a tank in 16 minutes and 24 minutes respectively. if both the pipes are opened simultaneously, after how much time should pipe x be closed so that the tank is full in 21 minutes?

Answer 1

let pipe x is closed after 'a' minutes
pipe x 1 min work = 1/16
pipe xa minutes work =a/16
pipe y 1 minute work = 1/24

now according to question
$\frac{a}{16} + \frac{21}{24} = 1 \\ \frac{3a + 42}{48} = 1 \\ 3a +42 = 48 \\ 3a = 6 \\ a = 2$
thus tank is filled in 21 minutes if pipe x is closed after 2 minutes