Question : Rama alone can do a work in 5 days working 4 hours a day. Seema alone can do the same work in 3 days working 10 hours a day. How many hours do they need to work together in a day to complete the same work in 6 days?
Option 1: 1 hour
Option 2: 3 hours
Option 3: 5 hours
Option 4: 2 hours
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Correct Answer: 2 hours
Solution :
Rama's work = 5 × 4 = 20 hours
Seema's work = 3 × 10 = 30 hours
Hourly work of Rama = $\frac{1}{20}$
Hourly work of Seema = $\frac{1}{30}$
Combined one hour work of Rama and Seema $=\frac{1}{20}+\frac{1}{30}=\frac{2+3}{60}=\frac{1}{12}$
If they want to finish the work in 6 days at the rate of $\frac{1}{12}$ per hour, they need to work hourly per day $=\frac{1}{6\times\frac{1}{12}}= 2$
Hence, the correct answer is 2 hours.
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