There are 6 working days in a regular week and for each day, the working hours are 10. A man earns Rs.2.10 per hour for regular work and Rs.4.20 per hour for overtime.If he earns Rs.525 in 4 weeks, how many hours did he work?

Options

A. 245
B. 285
C. 275
D. 255

Answer

To solve the problem step by step, we will break down the information given and calculate how many hours the man worked in total.

### Step 1: Calculate Regular Working Hours
The man works for 6 days a week and 10 hours each day. Therefore, in one week, the total regular working hours can be calculated as follows:

\[ \text{Regular Working Hours per Week} = \text{Days per Week} \times \text{Hours per Day} = 6 \times 10 = 60 \text{ hours} \]

### Step 2: Calculate Total Regular Working Hours in 4 Weeks
Since he works for 4 weeks, we can find the total regular working hours over this period:

\[ \text{Total Regular Working Hours} = \text{Regular Working Hours per Week} \times \text{Number of Weeks} = 60 \times 4 = 240 \text{ hours} \]

### Step 3: Set Up the Earnings Equation
The man earns Rs. 2.10 per hour for regular work and Rs. 4.20 per hour for overtime. Let \( x \) be the number of overtime hours he worked. His total earnings can be expressed as:

\[ \text{Total Earnings} = (\text{Regular Hours} \times \text{Rate per Hour}) + (\text{Overtime Hours} \times \text{Overtime Rate}) \]

Substituting the values we have:

\[ 525 = (240 \times 2.10) + (x \times 4.20) \]

### Step 4: Calculate Regular Earnings
First, calculate the earnings from regular hours:

\[ 240 \times 2.10 = 504 \]

### Step 5: Substitute Regular Earnings into the Equation
Now substitute this back into the earnings equation:

\[ 525 = 504 + (x \times 4.20) \]

### Step 6: Solve for Overtime Earnings
Rearranging the equation to isolate the overtime earnings:

\[ x \times 4.20 = 525 - 504 \]
\[ x \times 4.20 = 21 \]

### Step 7: Calculate Overtime Hours
Now, solve for \( x \):

\[ x = \frac{21}{4.20} \]

To simplify \( \frac{21}{4.20} \):

\[ x = \frac{21 \times 10}{42} = \frac{210}{42} = 5 \]

So, the man worked 5 hours of overtime.

### Step 8: Calculate Total Hours Worked
Now we can find the total hours worked by adding regular hours and overtime hours:

\[ \text{Total Hours Worked} = \text{Regular Hours} + \text{Overtime Hours} = 240 + 5 = 245 \text{ hours} \]

### Final Answer
The total hours the man worked in 4 weeks is **245 hours**.

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