Rohan can finish a piece of work in 8 hours, while Sunil can finish it in 4 hours. If they work together, how much time will they take to complete the work?

Introduction / Context: This is a classic two-person work problem. The combined work rate is the sum of individual rates; the total time is the reciprocal of that sum.

Given Data / Assumptions:

• Rohan alone = 8 hours ⇒ r(R) = 1/8 per hour.
• Sunil alone = 4 hours ⇒ r(S) = 1/4 per hour.

Concept / Approach: Combined rate r = 1/8 + 1/4 = 3/8 per hour. Time together = 1 / r = 8/3 hours = 2 2/3 hours.

Step-by-Step Solution: r(R+S) = 1/8 + 1/4 = 3/8 per hour. Time = 1 / (3/8) = 8/3 hours = 2 hours 40 minutes.

Verification / Alternative check: In 2 2/3 hours, work done = (3/8) * (8/3) = 1 full job, confirming correctness.

Why Other Options Are Wrong: 3 hours (too slow), 2 hours (too fast), 3 1/3 hours (too slow), 2 1/4 hours (too fast). Only 2 2/3 hours satisfies the exact rate sum inversion.

Common Pitfalls: Averaging times instead of adding rates; arithmetic mistakes when converting 8/3 hours to hours and minutes.

Final Answer: 2 2/3 hours