Varun and Raju, working together, can complete a job in 40 hours, whereas Varun alone can complete the same job in 50 hours. The…

Question

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:

1. A. 170
2. B. 150
3. C. 200 (Correct answer)
4. D. 190

Correct Answer

Option C — 200

Detailed Solution & Explanation

The correct answer is 200.

Key Points

• Raju's one-hour work $=\dfrac{1}{40}-\dfrac{1}{50}=\dfrac{5-4}{200}=\dfrac{1}{200}$.
• So Raju alone takes 200 hours.

Additional Information

• Work problems are solved in rates per unit time, which add: 1/40 for the pair, 1/50 for Varun, so 1/200 for Raju.
• The general relation is 1/A + 1/B = 1/T, and the combined time T is always shorter than either individual time — a useful sanity check.
• Alternatively use LCM units: take the job as 200 units, so the pair does 5 units/hour and Varun 4, leaving Raju 1 unit/hour.