A painter can paint an entire fence in 24 hours when working alone at a constant rate. After working for 6 hours, he takes a break and stops. What fraction of the fence is still left to be painted at that moment?

Introduction / Context:
This is a simple fraction-of-work problem involving a painter who can finish painting a fence in a given time. We are told how long he works before stopping and asked to find what fraction of the job remains unfinished. Such questions are common in aptitude tests and help reinforce the idea that the fraction of work done is directly proportional to the time spent when the rate is constant.

Given Data / Assumptions:

The painter can finish the entire fence in 24 hours when working alone.
He actually paints for only 6 hours before taking a break and stopping.
The painting rate is constant during the time he works.
The whole fence is considered as one complete job (1 unit).

Concept / Approach:
If a worker finishes a job in T hours, the fraction of the job completed per hour is 1/T. When the worker paints for t hours, the fraction of the job done is t/T. Subtracting this completed fraction from 1 gives the remaining fraction of the job. This approach is straightforward and only involves basic arithmetic and fractions.

Step-by-Step Solution:
Let the total work (whole fence) = 1 unit. The painter can complete 1 unit of work in 24 hours. So, his hourly work rate = 1/24 of the fence per hour. He actually works for 6 hours before stopping. Work completed in 6 hours = 6 * (1/24) = 6/24. Simplify 6/24 to 1/4 of the fence. Hence, fraction of the fence painted = 1/4. Remaining fraction of the fence = 1 - 1/4 = 3/4. Convert 3/4 to decimal form if needed: 3/4 = 0.75.

Verification / Alternative check:
As a quick check, if the painter requires 24 hours to complete the whole fence, then 6 hours is exactly one-fourth of the total required time. Therefore, it is logical that only one-fourth of the work is completed and three-fourths of the work is left. 3/4 written as a decimal is 0.75, which matches the result we computed.

Why Other Options Are Wrong:
Option 0.6 would mean only 60% of the fence remains, which is inconsistent with the one-fourth completed fraction of work.
Option 0.2 would indicate only 20% left, suggesting that 80% is already painted, which is clearly impossible after only one-fourth of the required time has been spent.
Option 0.8 means 80% of the fence is left, implying that only 20% has been painted, which does not match the 6/24 = 1/4 fraction actually done.
Option 0.5 would assume that half of the fence is left, which would correspond to 12 hours of work and not the given 6 hours.

Common Pitfalls:
A frequent error is to confuse the fraction of time spent with the fraction of work left instead of the fraction completed. Another mistake is performing incorrect fraction simplification, such as misreading 6/24 as 1/6 instead of 1/4. Always remember that with constant rate, time and completed work fraction are proportional, and double check arithmetic when simplifying fractions.

Final Answer:
Therefore, the fraction of the fence still left to be painted after 6 hours is 0.75, so the correct option is 0.75.