A can complete a piece of work in 15 days, B can complete the same work in 8 days, while B and C together can complete the work in 4 days. If A and C together can complete the work in $x$ days, and A and B together can complete it in $y$ days, then what is the value of $\frac{x}{y}$?

Explanation

$\therefore$ 1 day's work of (B + C) = $\frac{1}{4}$ 1 day's work of B = $\frac{1}{8}$ $\therefore$ 1 day's work of C = $\frac{1}{4} - \frac{1}{8} = \frac{1}{8}$ $\therefore$ (A + C)'s one day's work = $\frac{1}{15} + \frac{1}{8}$ = $\frac{23}{120}$ (A + B)'s one day's work = $\frac{1}{15} + \frac{1}{8}$ = $\frac{23}{120}$ $\therefore \frac{x}{y} = \frac{\frac{120}{23}}{\frac{23}{120}} \Rightarrow 1$