A constructor estimates that 4 workers can paint Mr Karthik house in 6 days, working at a constant rate. If instead he employs 5 workers, working at the same individual rate, how long will they take to complete the job?

Introduction / Context:
This is a simple time and work question about changing the number of workers assigned to a job. Knowing how long a given group of workers takes allows us to determine the total amount of work in worker days. We can then adjust the number of workers and compute the new time required.

Given Data / Assumptions:
• Four workers can paint the house in 6 days.
• All workers have identical constant work rates.
• We now use 5 workers instead of 4.
• The amount of work required to paint the house does not change.

Concept / Approach:
Total work can be expressed in worker days. If 4 workers take 6 days, the job corresponds to 4 × 6 worker days. When 5 workers are assigned, the same total work is divided by 5, giving the new number of days. This uses the direct inverse proportionality between number of workers and time when total work is fixed.

Step-by-Step Solution:
Step 1: Compute total work in worker days. Total work = number of workers × number of days = 4 × 6 = 24 worker days. Step 2: When 5 workers are assigned, let the required time be t days. Total work remains the same, so 5 × t = 24 worker days. Solve for t: t = 24 ÷ 5 = 24 / 5 days. As a mixed number, 24 / 5 = 4.8 days.

Verification / Alternative check:
We can interpret 4.8 days as 4 days and 0.8 of a day. In 4.8 days, 5 workers provide 5 × 4.8 = 24 worker days, exactly matching the original amount of work. Any shorter time would result in less total effort, while any longer time would exceed the required work.

Why Other Options Are Wrong:
Options like 3 days or 13 / 4 days give too few worker days and would not complete the job. For example, 5 workers in 3 days provide only 15 worker days. Likewise, 26 / 3 days or other values that do not simplify to 24 / 5 do not preserve the required total of 24 worker days.

Common Pitfalls:
A typical mistake is to scale days linearly, for example assuming that adding one worker reduces the time by exactly 1 day. The correct approach is to think in terms of total work in worker days and then use inverse proportion between number of workers and time taken.

Final Answer:
The job will be completed in 24/5 days.