While working 7 hour a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, 8 hour a day?

Answer: Option A

A can complete the work in 7 × 6 = 42 hours
1 hour's work of A = $$\frac{1}{42}$$
B can complete the work in 7 × 8 = 56 hours
1 hour's work of B = $$\frac{1}{56}$$
(A + B)'s 1 hour's work
$$\begin{array}{rl}& =\frac{1}{42}+\frac{1}{56}\\ & =\frac{4+3}{168}\\ & =\frac{7}{168}\end{array}$$
∴ Time taken by (A + B) working 8 hours daily
$$\frac{168}{7\times 8}=3\text{days}$$