George takes 8 hours to copy a 50-page manuscript while Sonia can copy the same manuscript in 6 hours. How many hours would it take them to copy a 100-page manuscript, if they work together ?

Answer: Option A

Number of pages typed by Gorge in 1 hour
$$\begin{array}{rl}& =\frac{50}{8}\\ & =\frac{25}{4}\end{array}$$
Number of pages typed by Sonia in 1 hour
$$\begin{array}{rl}& =\frac{50}{6}\\ & =\frac{25}{3}\end{array}$$
Number of pages typed by Gorge and Sonia together in 1 hour
$$\begin{array}{rl}& =\left(\frac{25}{4}+\frac{25}{3}\right)\\ & =\left(\frac{75+100}{12}\right)\\ & =\frac{175}{12}\\ & \therefore \text{Required time}\\ & =\left(100÷\frac{175}{12}\right)\text{hours}\\ & =\left(\frac{100\times 12}{175}\right)\text{ hours}\\ & =\frac{48}{7}\text{ hours}\\ & =6\frac{6}{7}\text{ hours}\end{array}$$