Ramesh, Dinesh and Ganesh completed a job in 12 days. They worked toge...
Given information:
- Ramesh, Dinesh, and Ganesh completed a job in 12 days.
- They worked together for 4 days and completed 44% of the total work.
- Ramesh quits the job at this point.
- The work done by Dinesh in 3 days is equal to the work done by Ganesh in 4 days.
Let's solve this step by step:
Step 1: Calculate the work done in 4 days
Since they completed 44% of the total work in 4 days, we can assume the total work to be 100%. Therefore, the work done in 4 days is 44%.
Step 2: Calculate the individual work rates
Let the work rate of Ramesh be R, Dinesh be D, and Ganesh be G.
Given that Dinesh completes the same work in 3 days as Ganesh does in 4 days, we can set up the following equation:
3D = 4G
Step 3: Calculate the work rates in terms of R
Since the work done by Ramesh, Dinesh, and Ganesh in 4 days is 44%, we can set up the following equation:
4R + 4D + 4G = 44%
Using the equation from Step 2, we can substitute G with (3/4)D:
4R + 4D + 4(3/4)D = 44%
4R + 4D + 3D = 44%
4R + 7D = 44%
Step 4: Calculate the work rates in terms of R
Since Ramesh quits the job after 4 days, the remaining work is completed by Dinesh and Ganesh. Therefore, the work done in 8 days by Dinesh and Ganesh is 100% - 44% = 56%.
Using the equation from Step 2, we can substitute G with (3/4)D:
8D + 8G = 56%
8D + 8(3/4)D = 56%
8D + 6D = 56%
14D = 56%
D = 4%
Step 5: Calculate the work rate of Ramesh
Using the equation from Step 3, we can substitute D with 4%:
4R + 7(4%) = 44%
4R + 28% = 44%
4R = 44% - 28%
4R = 16%
R = 4%
Step 6: Calculate the time taken by the fastest worker to complete the job
Since the work rate of Ramesh is 4%, the time taken by the fastest worker (Ramesh) to complete the job is 100% / 4% = 25 days.
Therefore, the correct answer is option A) 21.875 days, which is the closest approximation to 25 days.
Ramesh, Dinesh and Ganesh completed a job in 12 days. They worked toge...