$A$ can finish a work in $12$ days and $B$ can do it in $15$ days. After $A$ had worked for $3$ days, $B$ also joined $A$ to finish the remaining work. In how many days, the remaining work will be finished?

Answer is C

3 days * A’s work + x days * (A+B)’s work = 1

$3*\frac{1}{12}+x * (\frac{1}{12}+\frac{1}{15}) = 1$

$x * (\frac{1}{12}+\frac{1}{15}) = 1 - \frac{1}{4}$

$x = \frac{\frac{3}{4}}{\frac{9}{60}} = 5 days$