In a 5 day working week with 8 hours of regular work per day, a man is paid Rs. 2.40 per hour for regular work and Rs. 3.20 per hour for overtime. Over 4 such weeks he earns a total of Rs. 432. How many hours in total, including both regular hours and overtime, does he work?

Introduction / Context:
This problem tests the link between time, wage rate, and total earnings in a typical working week. We are given different hourly rates for regular work and overtime, along with the total earnings over several weeks. The task is to calculate the total number of hours worked, combining both regular and overtime hours, based on the pay structure and total income.

Given Data / Assumptions:

• There are 5 working days per week.
• Each working day has 8 regular working hours.
• Regular work is paid at Rs. 2.40 per hour.
• Overtime work is paid at Rs. 3.20 per hour.
• Total time considered is 4 weeks.
• Total earnings in 4 weeks are Rs. 432.

Concept / Approach:
First, we compute the total regular hours over 4 weeks and the corresponding regular wages. The difference between the total earnings and the regular wages must be the overtime pay. Using the overtime rate, we find the number of overtime hours. Finally, we add regular and overtime hours to obtain the total hours of work across the 4 week period.

Step-by-Step Solution:
Regular hours per week = 5 days * 8 hours per day = 40 hours.Regular hours in 4 weeks = 40 * 4 = 160 hours.Regular wages in 4 weeks = 160 * 2.40 = Rs. 384.Total earnings are Rs. 432, so overtime earnings = 432 - 384 = Rs. 48.Overtime rate is Rs. 3.20 per hour, so overtime hours = 48 / 3.20 = 15 hours.Total hours worked = regular hours + overtime hours = 160 + 15 = 175 hours.

Verification / Alternative check:
We can verify by recomputing earnings from the obtained hours. Regular wages: 160 hours * Rs. 2.40 = Rs. 384. Overtime wages: 15 hours * Rs. 3.20 = Rs. 48. Combined, 384 + 48 = Rs. 432, which matches the total income given in the question. Therefore, the calculated total time of 175 hours is correct and consistent with the data.

Why Other Options Are Wrong:
145 hours and 165 hours would imply smaller overtime hours and would not produce total earnings of Rs. 432 at the given pay rates. One hundred thirty five hours is even further from the required figure and leads to much less than Rs. 432. Only 175 hours leads to a correct split between regular earnings and overtime earnings that exactly matches the given total salary.

Common Pitfalls:
Candidates often forget to multiply the weekly hours by the number of weeks or may mistakenly assume that all hours are paid at the overtime rate. Another common error is to divide the total earnings directly by one of the hourly rates and ignore the fact that there are two different pay rates. Correctly separating regular pay and overtime pay is essential to obtaining the right answer.

Final Answer:
The man works for a total of 175 hours over the 4 week period.