Varun and Raju, working together, can complete a job in 40 hours whereas Varun alone can complete the same job in 50 hours. The number of hours required by Raju to complete the job alone is:

The correct answer is 200.

To find the time Raju needs to complete the job alone, we can analyze the rates of work for both Varun and Raju.

Let the total work to be completed be represented as 1 unit.

First, we determine the rate of work when Varun and Raju work together:
$\text{Combined rate of Varun and Raju}=\frac{1}{40}\text{of the job per hour}$

Next, we find the rate of work for Varun alone:
$\text{Varun's individual rate}=\frac{1}{50}\text{of the job per hour}$

Since their individual rates add up to their combined rate, we can write:
$\text{Raju's rate}=\text{Combined rate}-\text{Varun's rate}$

Substituting the rates into the equation:
$\text{Raju's rate}=\frac{1}{40}-\frac{1}{50}$

To subtract these fractions, we find the Least Common Multiple (LCM) of the denominators 40 and 50, which is 200:
$\text{Raju's rate}=\frac{5}{200}-\frac{4}{200}=\frac{1}{200}\text{of the job per hour}$

The time required for Raju to complete the job alone is the reciprocal of his individual rate:
$\text{Time required by Raju}=\frac{1}{1/200}=200\text{hours}$

Thus, Raju requires 200 hours to complete the job alone.