Work and Time Calculation
Problem Analysis
This problem requires calculating the time Ram needs to complete a task alone. We are given the combined time Ram and Shyam take together and the time Shyam takes alone.
Step-by-Step Solution
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Determine the work rates.
- Let the total work be 1 unit.
- The combined work rate of Ram and Shyam is $\frac{1}{6}$ task per day (since they finish together in 6 days).
- Shyam's work rate is $\frac{1}{8}$ task per day (since he finishes alone in 8 days).
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Calculate Ram's work rate.
Ram's rate = (Combined rate) - (Shyam's rate)
Ram's rate = $\frac{1}{6} - \frac{1}{8}$
Find a common denominator for 6 and 8, which is 24.
Ram's rate = $\frac{4}{24} - \frac{3}{24} = \frac{1}{24}$ task per day.
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Calculate the time Ram takes to finish the task alone.
Time = $\frac{\text{Total Work}}{\text{Individual Rate}}$
Time for Ram = $\frac{1}{\frac{1}{24}}$
Time for Ram = 24 days.
Conclusion
Ram will take 24 days to finish the task working alone.
Similar Questions
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Important Questions from Time and Work
Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?
A tank is filled in 8 hours by three taps A, B and C. The tap C is thrice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?
Had been one menless, then the number of days required to do a piece of work would have been one more. If the number of Man. Days required to complete the work is 56, how many workers were there?
A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it 12 hours. How long will B alone take to do it?
- lf 12 men can do a work in 20 days, in how many days will the work be done by 15 men-
