A mason can build a wall in 70 hours. After working continuously for 7 hours he takes a break. What fraction of the wall is still left to be built at that moment?

Introduction / Context:
This is a straightforward work and time question involving a single worker. We are told how long the worker takes to complete the entire job and asked what fraction of the job remains after working for a shorter number of hours. It directly uses the concept of proportional completion of work over time for a constant rate worker.

Given Data / Assumptions:

• The mason can complete the whole wall in 70 hours.
• He works for 7 hours and then stops.
• His working speed or rate remains constant.
• We are asked to find the fraction of the wall that is not yet built after these 7 hours.

Concept / Approach:
When a worker completes a job in T hours, in one hour the worker completes 1 / T of the job. Therefore, in t hours, the worker will complete t / T of the job. For this problem, we find the fraction of the job done in 7 hours and subtract this from 1 to obtain the incomplete fraction. The result is expressed as a decimal fraction, as shown in the options.

Step-by-Step Solution:
Step 1: Let the total work of building the wall be 1 unit.Step 2: Time required to complete the wall = 70 hours.Step 3: Therefore, in 1 hour, the mason completes 1 / 70 of the wall.Step 4: In 7 hours, the fraction of the wall completed = 7 * (1 / 70) = 7 / 70 = 1 / 10.Step 5: Fraction of the wall remaining = 1 - 1 / 10 = 9 / 10.Step 6: Express 9 / 10 as a decimal: 9 / 10 = 0.9.

Verification / Alternative check:
We can also note that 7 hours is exactly one tenth of the total required time, since 7 is 1 / 10 of 70. With a constant rate, in one tenth of the total time, the worker completes one tenth of the job. Thus 9 tenths remain, confirming that the fraction 0.9 is correct.

Why Other Options Are Wrong:

• 0.8: This suggests that only 0.2 of the work has been completed, which would correspond to 14 hours rather than 7 hours.
• 0.5: This would mean half the wall is completed, which would require 35 hours of work, not 7 hours.
• 0.75: This suggests only one quarter of the wall has been completed, which would be 17.5 hours of work, again inconsistent with 7 hours.

Common Pitfalls:
Some learners mistakenly divide the completed fraction as 7 / 70 and then forget to subtract from 1 to find what is left, or they confuse the fraction completed with the fraction remaining. Others might try to convert hours in an unnecessary way that complicates the calculation. The best approach is to work directly with fractions of the total time.

Final Answer:
The fraction of the wall still left to be built is 0.9.