X, Y and Z complete a work in 6 days. X or Y alone can do the same work in 16 days. In how many days Z alone can finish the same work ?

Answer: Option C

(X + Y)'s 1 day's work
$$\begin{array}{rl}& =\left(\frac{1}{16}+\frac{1}{16}\right)\\ & =\frac{2}{16}\\ & =\frac{1}{8}\end{array}$$
∴ Z's 1 day's work
(X + Y + Z)'s 1 day's work - (X + Y)'s 1 day's work
$$\begin{array}{rl}& =\frac{1}{6}-\frac{1}{8}\\ & =\frac{1}{24}\end{array}$$
∴ Z alone can finish the work in 24 days.