A labourer was engaged for a certain number of days for Rs. 8,500, but due to his absence for some days, he was paid Rs. 6,050 only. Find the number of days that he was absent.

Options

A. 49
B. 45
C. 44
D. 42

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
The laborer was supposed to be paid Rs. 8,500 for a certain number of days of work but was only paid Rs. 6,050 due to his absence. We need to find out how many days he was absent.

### Step 2: Calculate the Difference in Wages
First, we need to find the difference between the total wages he was supposed to receive and the wages he actually received.

\[ \text{Difference} = \text{Total Wages} - \text{Paid Wages} = 8500 - 6050 = 2450 \]

### Step 3: Determine the Daily Wage
Next, we need to find out how much he was being paid per day. To do this, we need to find out how many days he was supposed to work to earn Rs. 8,500.

Assuming he worked for \( x \) days, the daily wage can be calculated as:

\[ \text{Daily Wage} = \frac{8500}{x} \]

### Step 4: Calculate the Number of Days Absent
Since he was paid Rs. 6,050, we can find out how many days he actually worked. Let’s denote the number of days he worked as \( y \).

\[ \text{Paid Wages} = \text{Daily Wage} \times y \]

From the previous equation, we can substitute the daily wage:

\[ 6050 = \left(\frac{8500}{x}\right) \times y \]

### Step 5: Set Up the Equation
Now we can express \( y \) in terms of \( x \):

\[ y = \frac{6050 \cdot x}{8500} \]

### Step 6: Determine the Total Days Worked
The total days worked can be expressed as:

\[ \text{Total Days} = x \]

The number of days absent can be calculated as:

\[ \text{Days Absent} = x - y \]

Substituting \( y \):

\[ \text{Days Absent} = x - \frac{6050 \cdot x}{8500} \]

### Step 7: Simplify the Equation
Now we can simplify this:

\[ \text{Days Absent} = x \left(1 - \frac{6050}{8500}\right) \]

Calculating the fraction:

\[ 1 - \frac{6050}{8500} = \frac{8500 - 6050}{8500} = \frac{2450}{8500} = \frac{1}{3.47} \]

### Step 8: Calculate the Number of Days Absent
Now, if we assume \( x \) to be the total days he was supposed to work, we can find \( x \) based on the daily wage. Let’s assume he was supposed to work for a total of 30 days (this is an assumption for calculation):

\[ \text{Days Absent} = 30 \times \frac{2450}{8500} = 30 \times \frac{1}{3.47} \approx 8.64 \text{ days} \]

### Conclusion
Thus, the approximate number of days the laborer was absent is around 9 days (rounding off).