A labourer can complete a certain job in 50 hours. After working for 5 hours, he takes a break. What fraction of the job is still left to be completed at that moment?

Introduction / Context:
This is a straightforward time and work question that focuses on fractions of work done. We are told how long a labourer takes to finish a job if he works alone, and we are asked to find what fraction of the job remains after he works for a shorter period. This is a basic but important concept in many aptitude problems involving work and time.

Given Data / Assumptions:
- A labourer can complete the entire job in 50 hours. - He works continuously for 5 hours before taking a break. - His work rate remains constant over time. - We treat the total job as one complete unit of work.

Concept / Approach:
If a worker completes one full job in T hours, then the fraction of work done per hour is 1 / T. Therefore, the fraction of work completed in t hours is t / T. The remaining fraction of work is then 1 minus the fraction already completed. Here we use this idea with T = 50 hours and t = 5 hours to find the remaining part of the job.

Step-by-Step Solution:
Step 1: Time taken to complete the entire job = 50 hours. Step 2: Fraction of work done per hour = 1 / 50 of the job. Step 3: Time actually worked before the break = 5 hours. Step 4: Fraction of job completed in 5 hours = 5 * (1 / 50) = 5 / 50 = 1 / 10. Step 5: Remaining fraction of the job = 1 - 1 / 10 = 9 / 10. Step 6: In decimal form, 9 / 10 = 0.9.

Verification / Alternative check:
We can verify by thinking proportionally. Five hours is 5 / 50 = 1 / 10 of the total required 50 hours. Since work done is directly proportional to time worked in this kind of problem, the labourer completes 1 / 10 of the job. That automatically means 9 / 10 of the job remains, which is 0.9 as a decimal. This matches our calculation exactly.

Why Other Options Are Wrong:
0.8: This would mean only 80 percent of the job is left, implying that 20 percent is done, which would correspond to 10 hours of work, not 5 hours.
0.5: This would mean half the job is left, which would require 25 hours of work, not just 5 hours.
0.75: This corresponds to 3 / 4 of the job left, again inconsistent with only 5 hours of work done out of 50 hours total.
0.6: This would indicate 60 percent remaining and 40 percent completed, which is more than what 5 hours of work can achieve out of 50 hours total.

Common Pitfalls:
A frequent error is mixing up the fractions of work done and remaining. Students might mistakenly treat 5 hours as a large portion of 50 hours or miscompute the fraction 5 / 50. Ensure accurate fraction simplification and remember that the remaining fraction is always 1 minus the completed fraction. Carefully translating time into fraction of work is the crucial step.

Final Answer:
The fraction of the job still left to be completed is 0.9.