Ravi and Sanju together can do a job in 2 days, Sanju and Mahesh can do it in 4 days, while Ravi and Mahesh can do it in 2 days. What is the number of days required for Ravi to do the same job alone?

The correct answer is $\frac{8}{3}$ days.

Step-by-Step Explanation:

Let us denote the 1-day work rates of Ravi, Sanju, and Mahesh by $R$, $S$, and $M$ respectively.

From the given problem, we can express the combined work done in 1 day for each pair:

1. Ravi and Sanju complete the job in 2 days, so their combined 1-day work rate is:

$R+S=\frac{1}{2}$

2. Sanju and Mahesh complete the job in 4 days, so their combined 1-day work rate is:

$S+M=\frac{1}{4}$

3. Ravi and Mahesh complete the job in 2 days, so their combined 1-day work rate is:

$R+M=\frac{1}{2}$

Now, add all three equations together:

$(R+S)+(S+M)+(R+M)=\frac{1}{2}+\frac{1}{4}+\frac{1}{2}$

$2(R+S+M)=\frac{2}{4}+\frac{1}{4}+\frac{2}{4}$

$2(R+S+M)=\frac{5}{4}$

Dividing both sides by 2 gives the total 1-day work rate when all three work together:

$R+S+M=\frac{5}{8}$

To find the 1-day work rate of Ravi alone ($R$), subtract the combined 1-day work rate of Sanju and Mahesh ($S+M$) from the total 1-day work rate:

$R=(R+S+M)-(S+M)$

$R=\frac{5}{8}-\frac{1}{4}$

$R=\frac{5}{8}-\frac{2}{8}=\frac{3}{8}$

Thus, Ravi alone completes $\frac{3}{8}$ of the total job per day.

The total number of days required for Ravi to finish the job alone is the reciprocal of his 1-day work rate:

$\text{Days required}=\frac{1}{R}=\frac{8}{3}$

Therefore, the number of days required for Ravi to do the job alone is $\frac{8}{3}$ days.