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 ?
A. $$6\frac{6}{7}\,\,{\text{hours}}$$
B. $${\text{9 hours}}$$
C. $$9\frac{5}{7}\,\,{\text{hours}}$$
D. $${\text{14 hours}}$$
Answer: Option A
Solution(By Examveda Team)
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
$$\eqalign{ & = \left( {\frac{{25}}{4} + \frac{{25}}{3}} \right) \cr & = \left( {\frac{{75 + 100}}{{12}}} \right) \cr & = \frac{{175}}{{12}} \cr & \therefore {\text{Required time}} \cr & = \left( {100 \div \frac{{175}}{{12}}} \right){\text{hours}} \cr & = \left( {\frac{{100 \times 12}}{{175}}} \right){\text{ hours}} \cr & = \frac{{48}}{7}{\text{ hours}} \cr & = 6\frac{6}{7}{\text{ hours}} \cr} $$
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