Rajesh can complete a job in 18 days. Rohit is 50% more skilled than Rajesh. Find the total time taken to do the same job when they both work together.
Question
Rajesh can complete a job in 18 days. Rohit is 50% more skilled than Rajesh. Find the total time taken to do the same job when they both work together.
Solution
Step 1: Identify the time taken by each person to complete the job individually.
We know that Rajesh can complete the job in 18 days.
Step 2: Determine how much time Rohit would take to complete the job.
Since Rohit is 50% more skilled than Rajesh, he would take 50% less time than Rajesh to complete the job. So, Rohit would take 18 days - (50/100)*18 days = 9 days to complete the job.
Step 3: Calculate the combined rate of work for Rajesh and Rohit.
The rate of work is the reciprocal of the time taken to complete the job. So, Rajesh's rate of work is 1/18 jobs/day and Rohit's rate of work is 1/9 jobs/day.
When they work together, their combined rate of work is 1/18 + 1/9 = 1/6 jobs/day.
Step 4: Find the total time taken to do the job when they both work together.
The total time taken to do the job when they both work together is the reciprocal of their combined rate of work. So, the total time taken is 1 / (1/6) = 6 days.
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