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Question 59

George takes 8 hours to copy a 50 page manuscript while Sonya 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?

Solution

George takes 8 hours to copy a 50 page manuscript, => Efficiency of George = $$\frac{50}{8}=\frac{25}{4}$$ pages/hr

Similarly, Sonya's efficiency = $$\frac{50}{6}=\frac{25}{3}$$ pages/hr

=> Work done by them working together in 1 hr = $$\frac{25}{3}+\frac{25}{4}=\frac{175}{12}$$

$$\therefore$$ Time taken when they work together to finish a 100 page manuscript = $$\frac{100}{\frac{175}{12}}$$

= $$100\times\frac{12}{175}=\frac{48}{7}=6\frac{6}{7}$$ hours

=> Ans - (A)

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