In a week, there are 5 working days and each workers has to work 8 hours per day. A worker gets 2.40 per working and 3.20 per extra hour. If he earned 432 in 4 weeks then how many hour he worked?

Options

A. 160
B. 175
C. 180
D. 195

Answer

To solve the problem step by step, let's break it down:

### Step 1: Calculate the total working hours in 4 weeks
A worker works 5 days a week and 8 hours each day. Therefore, in one week, the total working hours can be calculated as:
\[ \text{Total working hours in one week} = \text{Number of days} \times \text{Hours per day} = 5 \times 8 = 40 \text{ hours} \]
In 4 weeks, the total working hours will be:
\[ \text{Total working hours in 4 weeks} = 40 \times 4 = 160 \text{ hours} \]

### Step 2: Set up the earnings equation
The worker earns 2.40 rupees per hour for regular working hours and 3.20 rupees per hour for extra hours. Let \( x \) be the total regular working hours (which we calculated as 160 hours) and \( y \) be the extra hours worked. The total earnings can be expressed as:
\[ \text{Total earnings} = (\text{Earnings from working hours}) + (\text{Earnings from extra hours}) \]
This can be written as:
\[ 432 = (2.40 \times x) + (3.20 \times y) \]
Substituting \( x = 160 \):
\[ 432 = (2.40 \times 160) + (3.20 \times y) \]

### Step 3: Calculate the earnings from regular hours
Calculating the earnings from the regular working hours:
\[ 2.40 \times 160 = 384 \text{ rupees} \]
Now substituting this back into the earnings equation:
\[ 432 = 384 + (3.20 \times y) \]

### Step 4: Solve for extra hours \( y \)
Rearranging the equation to isolate \( y \):
\[ 432 - 384 = 3.20 \times y \]
\[ 48 = 3.20 \times y \]
Now, divide both sides by 3.20 to find \( y \):
\[ y = \frac{48}{3.20} = 15 \text{ hours} \]

### Step 5: Calculate total hours worked
The total hours worked \( T \) is the sum of regular hours and extra hours:
\[ T = x + y = 160 + 15 = 175 \text{ hours} \]

### Final Answer
The total number of hours the worker worked is **175 hours**.

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