In a regular week there are 5 working days, each with 8 regular working hours. A man is paid Rs 2.40 per hour for regular hours and Rs 3.20 per hour for overtime. In 4 such weeks he earns a total of Rs 432. For how many hours in total, including both regular and overtime hours, does he work in these 4 weeks?

Introduction / Context:
This problem is a classic wages and work question from quantitative aptitude. It combines the concept of regular working hours with overtime and different hourly rates. Such problems are very common in bank exams, SSC exams, and placement tests, and they are meant to check whether you can construct a linear equation from a word description involving time, rate of pay, and total earnings. The key idea is to separate regular hours, which are fixed for 4 weeks, from overtime hours, which are unknown, and then use the total income to find the extra hours worked.

Given Data / Assumptions:

• There are 5 working days in a regular week.
• Each working day has 8 regular working hours.
• The worker is paid Rs 2.40 per regular hour.
• The worker is paid Rs 3.20 per overtime hour.
• The period considered is 4 such weeks.
• Total earnings in 4 weeks are Rs 432.

Concept / Approach:
The approach is to first calculate the total regular working hours in 4 weeks and the corresponding income from those hours. Then, one introduces a variable for the overtime hours, calculates the overtime earnings in terms of that variable, and sets the sum equal to the known total income. This results in a simple linear equation with one unknown, namely the overtime hours. After solving for the overtime hours, we add them to the fixed regular hours to obtain the total hours worked in 4 weeks.

Step-by-Step Solution:
Regular hours in one week = 5 days * 8 hours per day = 40 hours. Regular hours in 4 weeks = 4 * 40 = 160 hours. Let the total overtime hours in 4 weeks be x hours. Regular pay for 160 hours = 160 * 2.40 = Rs 384. Overtime pay for x hours = x * 3.20. Total earnings are given as 432, so: 384 + 3.20 * x = 432. Subtract 384 from both sides: 3.20 * x = 432 - 384 = 48. So, x = 48 / 3.20 = 15 hours. Total hours worked in 4 weeks = regular hours + overtime hours = 160 + 15 = 175 hours.

Verification / Alternative check:
To verify, compute the income from 175 total hours, with the first 160 counted at the regular rate and the remaining 15 as overtime. Regular income remains 160 * 2.40 = 384. Overtime income is 15 * 3.20 = 48. The total income is therefore 384 + 48 = 432, which matches the given total earning. This confirms that the computed overtime hours and thus the total working hours are correct.

Why Other Options Are Wrong:
160 hours: This would correspond to no overtime at all, giving only 160 * 2.40 = Rs 384, which is less than 432.
180 hours: This implies 20 overtime hours, giving extra 20 * 3.20 = 64, so total earnings would be 384 + 64 = 448, which is too high.
195 hours: This means 35 overtime hours and earnings 384 + 35 * 3.20 = 496, again not 432.
200 hours: This would mean 40 overtime hours and total income 384 + 40 * 3.20 = 512, far from the given value.

Common Pitfalls:
A common mistake is to treat all hours as if they are paid at a single rate, which ignores the concept of overtime and leads to a wrong equation. Another frequent error is miscounting the number of regular hours by forgetting that there are 4 weeks or miscalculating 5 days * 8 hours. Some students also incorrectly divide by 2.4 instead of 3.2 when solving for the overtime hours. Careful reading of the rates and correct identification of the unknown variable are essential.

Final Answer:
The man works a total of 175 hours in the 4 weeks, including both regular and overtime hours.