Ram can complete a piece work in 15 days, Rohan in 25 days, and Rohit in 30 days. Rohan and Rohit worked together for 2 days and then Rohit was replaced by Ram. In how many days altogether was the work completed?

Correct option is A

Given:
Ram can complete the work in 15 days.
Rohan can complete the work in 25 days.
Rohit can complete the work in 30 days.
Rohan and Rohit worked together for 2 days and then Rohit was replaced by Ram.
Formula Used:
Work rate = 1 / (number of days to complete the work)
Total work done = Work rate × Time
Solution:
1. Calculate the work rates:
Work rate of Ram = 1 / 15
Work rate of Rohan = 1 / 25
Work rate of Rohit = 1 / 30
2. Calculate the work done by Rohan and Rohit in 2 days:
Combined work rate of Rohan and Rohit = (1 / 25) + (1 / 30)
Combined work rate of Rohan and Rohit = (6 + 5) / 150 = 11 / 150
Work done by Rohan and Rohit in 2 days = (11 / 150) × 2 = 22 / 150 = 11 / 75
3. Calculate the remaining work:
Total work = 1
Remaining work = 1 - (11 / 75) = 64 / 75
4. Calculate the time taken by Rohan and Ram to complete the remaining work:
Combined work rate of Rohan and Ram = (1 / 25) + (1 / 15)
Combined work rate of Rohan and Ram = (3 + 5) / 75 = 8 / 75
Time taken to complete the remaining work = (Remaining work) / (Combined work rate)
Time = (64 / 75) / (8 / 75) = 64 / 8 = 8 days
5. Calculate the total time taken to complete the work:
Total time = Time worked by Rohan and Rohit + Time worked by Rohan and Ram
Total time = 2 days + 8 days = 10 days
Alternate Method: