A labourer is engaged for 20 days on the condition that he will receive ₹120 for each day he works and will be fined ₹10 for each day he is absent. If he receive 1880 in all, for how many days did he remains absent?

Options

A. 2 days
B. 12 days
C. 10 days
D. 4 days

Answer

To solve the problem, we need to determine how many days the laborer was absent based on the information provided.

### Step-by-step Solution:

1. **Define Variables**:
Let \( x \) be the number of days the laborer worked. Since he was engaged for 20 days, the number of days he was absent will be \( 20 - x \).

2. **Calculate Earnings**:
The laborer earns ₹120 for each day he works. Therefore, his total earnings from working \( x \) days will be:
\[ \text{Earnings from work} = 120x \]

3. **Calculate Fines**:
The laborer is fined ₹10 for each day he is absent. Thus, the total fines for \( 20 - x \) days of absence will be:
\[ \text{Fines for absence} = 10(20 - x) = 200 - 10x \]

4. **Set Up the Equation**:
According to the problem, the total amount received by the laborer after working and being fined is ₹1880. Therefore, we can set up the equation:
\[ \text{Total Earnings} - \text{Total Fines} = 1880 \]
Substituting the expressions we found:
\[ 120x - (200 - 10x) = 1880 \]

5. **Simplify the Equation**:
Simplifying the equation gives:
\[ 120x - 200 + 10x = 1880 \]
Combine like terms:
\[ 130x - 200 = 1880 \]

6. **Isolate \( x \)**:
Add 200 to both sides:
\[ 130x = 1880 + 200 \]
\[ 130x = 2080 \]

7. **Solve for \( x \)**:
Divide both sides by 130:
\[ x = \frac{2080}{130} \]
\[ x = 16 \]

8. **Calculate Days Absent**:
Since \( x = 16 \), the number of days the laborer was absent is:
\[ 20 - x = 20 - 16 = 4 \]

### Final Answer:
The laborer was absent for **4 days**.