A person was appointed for a 50 days job on a condition that he will be paid Rs. 12 for every working day but he will be fined Rs. 6 for every day he remains absent. After the completion of the work, he got Rs. 420. For how many days, he did not work?

Options

A. 15 days
B. 5 days
C. 10 days
D. 20 days

Answer

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

### Step 1: Define Variables
Let \( X \) be the number of days the person did not work. Since the total duration of the job is 50 days, the number of days he worked will be \( 50 - X \).

**Hint:** Define variables to represent unknown quantities in the problem.

### Step 2: Calculate Earnings and Fines
The person earns Rs. 12 for each working day. Therefore, his earnings for the days he worked is:
\[ \text{Earnings} = (50 - X) \times 12 \]
He is fined Rs. 6 for each day he is absent. Thus, his total fines for the days he did not work is:
\[ \text{Fines} = X \times 6 \]

**Hint:** Use the information given in the problem to set up expressions for earnings and fines.

### Step 3: Set Up the Equation
The total amount he received after completing the work is Rs. 420. Therefore, we can set up the equation:
\[ \text{Earnings} - \text{Fines} = 420 \]
Substituting the expressions from Step 2:
\[ (50 - X) \times 12 - X \times 6 = 420 \]

**Hint:** Relate the earnings and fines to the total amount received to form an equation.

### Step 4: Simplify the Equation
Now, let's simplify the equation:
\[ 600 - 12X - 6X = 420 \]
Combine like terms:
\[ 600 - 18X = 420 \]

**Hint:** Simplifying the equation helps in isolating the variable.

### Step 5: Solve for \( X \)
Next, we will isolate \( X \):
\[ 600 - 420 = 18X \]
\[ 180 = 18X \]
Dividing both sides by 18 gives:
\[ X = 10 \]

**Hint:** Isolate the variable to find its value.

### Conclusion
The number of days the person did not work is \( X = 10 \).

**Final Answer:** The person did not work for **10 days**.