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?

The correct answer is 10 days.

Let's solve the problem step-by-step by finding the individual rates of work (efficiencies) of Ram, Rohan, and Rohit.

Step 1: Determine the total work
We can assume the total work is the Least Common Multiple (LCM) of the days taken by Ram (15 days), Rohan (25 days), and Rohit (30 days).
LCM of 15, 25, and 30 is 150.
So, let the total work be 150 units.

Step 2: Calculate the daily work (efficiency) of each person
Daily work of Ram =
$\frac{150}{15}=10$
units per day.
Daily work of Rohan =
$\frac{150}{25}=6$
units per day.
Daily work of Rohit =
$\frac{150}{30}=5$
units per day.

Step 3: Calculate the work done in the first 2 days
Rohan and Rohit worked together for the first 2 days.
Combined daily work of Rohan and Rohit =
$6+5=11$
units per day.
Work completed in 2 days =
$11\times 2=22$
units.

Step 4: Find the remaining work
Remaining work =
$150-22=128$
units.

Step 5: Calculate the time taken to complete the remaining work
Rohit is replaced by Ram, so Rohan and Ram work together to complete the remaining work.
Combined daily work of Rohan and Ram =
$6+10=16$
units per day.
Number of days Rohan and Ram work to complete the remaining 128 units =
$\frac{128}{16}=8$
days.

Step 6: Calculate the total days to complete the work
Total days = Days worked by Rohan and Rohit + Days worked by Rohan and Ram
Total days =
$2+8=10$
days.