Question : Disha takes 12 hours to copy a 75-page manuscript, while Mohit can copy the same manuscript in 10 hours. How many hours will it take for them to copy a 150-page manuscript if they work together?
Option 1: $10 \frac{10}{11}$ hours
Option 2: $9 \frac{9}{11}$ hours
Option 3: $8 \frac{9}{11}$ hours
Option 4: $11 \frac{8}{11}$ hours
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Correct Answer: $10 \frac{10}{11}$ hours
Solution :
Given: Time taken by Disha = 12 hours
Time taken by Mohit = 10 hours
Total work = LCM of (12, 10) = 60 units
60 units = 75 pages
⇒ 120 units = 150 pages
Efficiency of Disha = $\frac{60}{12}$ = 5
Efficiency of Mohit = $\frac{60}{10}$ = 6
If they work together, the time taken to complete the work,
= $\frac{120}{5+6}=10 \frac{10}{11}$ hours
Hence, the correct answer is $10 \frac{10}{11}$ hours.
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