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?

Explanation:-

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
$$\eqalign{ & = \frac{1}{{42}} + \frac{1}{{56}} \cr & = \frac{{4 + 3}}{{168}} \cr & = \frac{7}{{168}} \cr}$$
∴ Time taken by (A + B) working 8 hours daily
$$\frac{{168}}{{7 \times 8}} = 3\,{\text{days}}$$