a) $$6\frac{6}{7}\,\,{\text{hours}}$$
b) $${\text{9 hours}}$$
c) $$9\frac{5}{7}\,\,{\text{hours}}$$
d) $${\text{14 hours}}$$

Answer: a
Explanation: Number of pages typed by Gorge in 1 hour
$$\eqalign{ & = \frac{{50}}{8} \cr & = \frac{{25}}{4} \cr} $$
Number of pages typed by Sonia in 1 hour
$$\eqalign{ & = \frac{{50}}{6} \cr & = \frac{{25}}{3} \cr} $$
Number of pages typed by Gorge and Sonia together in 1 hour
$$\eqalign{ & = \left( {\frac{{25}}{4} + \frac{{25}}{3}} \right) \cr & = \left( {\frac{{75 + 100}}{{12}}} \right) \cr & = \frac{{175}}{{12}} \cr & {\text{Required time}} \cr & = \left( {100 \div \frac{{175}}{{12}}} \right){\text{hours}} \cr & = \left( {\frac{{100 \times 12}}{{175}}} \right){\text{ hours}} \cr & = \frac{{48}}{7}{\text{ hours}} \cr & = 6\frac{6}{7}{\text{ hours}} \cr} $$