To solve this problem, let's first calculate the rate at which the painters work.
We are given that 5 painters can complete the job in 8 days. This means that the total work done by the painters is 1 job.
Let "R" represent the rate of work done by each painter. Therefore, the rate at which 5 painters work together is 5R.
We can set up the following equation to represent the work done in 8 days:
[5R \times 8 = 1]
Simplifying this equation, we have:
[40R = 1]
Now, let's consider the scenario when 5 more painters join the team after 4 days.
The initial 5 painters worked for 4 days, so the amount of work done by them is (5R \times 4 = 20R).
The remaining work to be done is (1 - 20R).
Now, the total number of painters is 5 + 5 = 10 painters.
We can set up the following equation to represent the work done by the 10 painters:
[10R \times D = 1 - 20R]
where "D" represents the number of additional days required to complete the job.
Simplifying this equation, we have:
[10RD = 1 - 20R]
Since we want to find the number of additional days required to complete the job, we need to find the value of "D".
To solve for "D", let's substitute the value of (R) from the first equation into the second equation:
[10 \times \frac{1}{40} \times D = 1 - 20 \times \frac{1}{40}]
Simplifying this equation, we have:
[\frac{D}{4} = 1 - \frac{1}{2}]
[\frac{D}{4} = \frac{1}{2}]
Multiplying both sides of the equation by 4, we get:
[D = 2]
Therefore, it will take an additional 2 days to complete the job.
The correct answer is option D) 2.