A person is paid Rs 150 for each day he works and is find Rs 30 for each day he remains absent. If in 40 days, he earned Rs 3,300, find for how many days did he work?

Answer

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

### Step 1: Define Variables
Let \( X \) be the number of days the person worked.

### Step 2: Calculate Days Absent
Since the total number of days is 40, the number of days he remained absent will be \( 40 - X \).

### Step 3: Calculate Earnings
The earnings from working for \( X \) days at Rs 150 per day is:
\[ 150X \]

### Step 4: Calculate Fines
The fines for being absent for \( 40 - X \) days at Rs 30 per day is:
\[ 30(40 - X) \]

### Step 5: Set Up the Equation
According to the problem, the total earnings after 40 days is Rs 3,300. Therefore, we can set up the equation:
\[ 150X - 30(40 - X) = 3300 \]

### Step 6: Simplify the Equation
Expanding the equation:
\[ 150X - 1200 + 30X = 3300 \]
Combining like terms:
\[ 180X - 1200 = 3300 \]

### Step 7: Move Constant to the Right Side
Adding 1200 to both sides:
\[ 180X = 3300 + 1200 \]
\[ 180X = 4500 \]

### Step 8: Solve for \( X \)
Dividing both sides by 180:
\[ X = \frac{4500}{180} \]
Simplifying:
\[ X = 25 \]

### Conclusion
The person worked for **25 days**.

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