One day, Rahul started a work at 9 AM and Gautam joined him two hours later. They then worked together and completed the work at 5 PM the same day. If both had started at 9 AM and worked together, the work would have been completed 30 minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is
Started 2 weeks ago by Shashank in
Explanatory Answer
Let R be the fraction of work done by Rahul in 1 hour.
and G be the fraction of work done by Gautam in 1 hour.
Initially Rahul works from 9AM to 5PM (8 hours) and Gautam works for 2 hours less.
8R + 6G = 1 whole unit of work
If they start together they finish 30 minutes earlier or if they start at 9 AM, they finish at 4:30PM (7.5 hours)
7.5R + 7.5G = 1 whole unit of work
8R + 6G = 7.5R + 7.5G
0.5R = 1.5G
R = 3G
This means Rahul is thrice as efficient as Gautam.
8R + 6G = 1 whole unit of work
8R + 2R = 1 whole unit of work
10R = 1 whole unit of work
R is the fraction of work done by Rahul in 1 hour.
Since 10R = 1
R alone takes 10 hours to finish the job.
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