The question in the image provides the following scenario:

• 42 workers are painting a wall with a target to complete the job in 36 days.
• On the 7th day, work stopped due to rain for a total of 3 days.
• On the 20th day, work stopped again for 2 days because they ran out of materials.
• Despite the delays, the job must be completed within the original 36-day deadline.
• The question asks how many additional workers are needed to meet the original deadline.

Step-by-step Solution:

1. Initial Work Rate:

   • The total number of worker-days required to complete the job is $42 \text{ workers} \times 36 \text{ days} = 1512 \text{ worker-days}$.

2. Work Halted:

   • On the 7th day, the work stopped for 3 days due to rain. So, no work was done on days 7, 8, and 9. They resumed work on day 10.
   • On the 20th day, work stopped again for 2 days due to a lack of materials. So, no work was done on days 20 and 21. Work resumed on day 22.

   Therefore, a total of $3 + 2 = 5$ days were lost due to these interruptions.

3. Remaining Work Time:

   • Since the total target was to finish in 36 days, the workers now only have $36 - 5 = 31$ working days to finish the job.

4. Work Rate Adjustment:

   • The job requires 1512 worker-days in total, and after the delays, only 31 days remain.
   • Let $x$ be the new required number of workers. The equation is: $x \times 31 = 1512$ Solving for $x$: $x = \frac{1512}{31} \approx 48.77$ Since the number of workers must be a whole number, we round $x$ up to 49 workers.

5. Additional Workers Needed:

   • Initially, there were 42 workers. Now, we need 49 workers, so the number of additional workers required is: $49 - 42 = 7 \text{ additional workers}$

Answer:

The number of additional workers needed is 7.

Would you like more details or have any questions about the solution?

Here are 5 related questions to further your understanding:

1. What happens if only 6 additional workers are added instead of 7?
2. How would the answer change if there was only a 4-day delay instead of 5 days?
3. How can you calculate the daily productivity rate of each worker?
4. What if the target was extended by 5 days due to delays?
5. How would the solution differ if fewer than 42 workers started the project?

Tip: When calculating worker-days, always break down the total work required before adjusting for interruptions.