Given information:

- Ram takes 9 days to complete a piece of work.
- Suraj takes 12 days to complete the same work.
- Ram has already worked for 2 days before Suraj joined him.

Calculating the individual work rates:

Let's assume that the total work is represented by the variable "W".

From the given information, we can calculate the work done by Ram in a day and Suraj in a day:

- Ram's work rate = W/9
- Suraj's work rate = W/12

Calculating the work done by Ram in 2 days:

As Ram has already worked for 2 days before Suraj joined him, we can calculate the work done by Ram in those 2 days:

Work done by Ram in 2 days = 2 * (W/9) = 2W/9

Calculating the remaining work:

The remaining work after Ram worked for 2 days can be calculated as:

Remaining work = Total work - Work done by Ram in 2 days = W - (2W/9) = (9W - 2W)/9 = 7W/9

Calculating the time taken to complete the remaining work:

Now, we need to calculate the time taken by both Ram and Suraj together to complete the remaining work (7W/9).

Since we know their individual work rates, we can create the following equation:

(Work done by Ram in 1 day * Time taken by Ram) + (Work done by Suraj in 1 day * Time taken by Suraj) = Remaining work

((W/9) * Time taken by Ram) + ((W/12) * Time taken by Suraj) = 7W/9

Calculating the time taken by Ram and Suraj together:

Since Ram has already worked for 2 days, the remaining time taken by Ram is (Time taken by Ram - 2).

Substituting the values into the equation, we get:

((W/9) * (Time taken by Ram - 2)) + ((W/12) * Time taken by Suraj) = 7W/9

Simplifying the equation:

Simplifying the equation, we get:

((W/9) * Time taken by Ram) - ((2W/9) + (W/12) * Time taken by Suraj) = 7W/9

((W/9) * Time taken by Ram) + (W/12) * Time taken by Suraj = 7W/9 + 2W/9

((W/9) * Time taken by Ram) + (W/12) * Time taken by Suraj = (9W + 2W)/9

((W/9) * Time taken by Ram) + (W/12) * Time taken by Suraj = 11W/9

Solving the equation:

To solve the equation, we can use the concept of least common multiple (LCM).

The LCM of 9 and