Abhinav is twice as efficient a workman as Balwant and therefore completes a certain job in 36 days less than Balwant. If both Abhinav and Balwant work together on this job, in how many days will they complete it?

Introduction / Context:
This question tests the relation between efficiency and time taken to complete a job. One worker is said to be twice as efficient as another, and the difference in their times to finish the same job is given. From this, we find each worker's individual time and then their combined time when they work together. Such ratio based time and work questions are very common in aptitude tests.

Given Data / Assumptions:
- Abhinav is twice as efficient as Balwant, that is Abhinav's rate is double Balwant's rate.
- Because of this higher efficiency, Abhinav finishes the job in 36 days less than Balwant.
- Work rate is constant for both workers.
- Total work is one complete job.

Concept / Approach:
Efficiency is inversely proportional to the time taken to complete a fixed amount of work. If Abhinav is twice as efficient as Balwant, Abhinav takes half the time Balwant takes. We use the given difference of 36 days between their times to set up an equation, solve for each individual time, then convert these times into daily work rates. Finally we add the rates to compute the combined time when both work together.

Step-by-Step Solution:
Step 1: Let Balwant alone take B days to complete the job. Step 2: Since Abhinav is twice as efficient, he will take B/2 days to finish the same job. Step 3: Given that Balwant's time minus Abhinav's time is 36 days, so B − B/2 = 36. Step 4: B/2 = 36, hence B = 72 days. Step 5: Therefore Abhinav's time = B/2 = 36 days. Step 6: Abhinav's daily rate = 1/36, Balwant's daily rate = 1/72. Step 7: Combined rate when working together = 1/36 + 1/72 = 3/72 = 1/24. Step 8: Time taken together = 1 / (1/24) = 24 days.

Verification / Alternative check:
Check the difference in times: Balwant takes 72 days, Abhinav takes 36 days, and 72 − 36 = 36 days, which matches the problem statement. Also, if together they take 24 days, then in 24 days Abhinav does 24 * 1/36 = 2/3 of the work and Balwant does 24 * 1/72 = 1/3 of the work. Total work done is 2/3 + 1/3 = 1 complete job. This fully confirms the result.

Why Other Options Are Wrong:
Option 12 days: This would imply a combined rate too high compared with the individual times of 72 and 36 days.
Option 6 days: Far too small and unrealistic relative to each worker's solo time.
Option 18 days: Does not satisfy the sum of their daily rates when rechecked and would imply they are faster than their actual efficiencies allow.

Common Pitfalls:
Some learners confuse twice the efficiency with twice the time. Remember that if one person is twice as efficient, time taken becomes half. Another pitfall is to add or subtract times directly rather than converting to rates. Always move from time to rate (1/time), combine those, then invert to get the final time.

Final Answer:
Abhinav and Balwant together will complete the job in 24 days.