A man engaged a servant on a condition that he would pay him Rs. 80 and a pair of jeans after service of one year. Servant served for only 9 months and receives a pair of jeans and an amount of Rs. 55. The price (in Rs) of the jeans is ________.

Options

A. Rs. 80
B. Rs. 60
C. Rs. 40
D. Rs. 20

Answer

To find the price of the jeans, we can follow these steps:

### Step 1: Define the variables
Let the price of the jeans be \( X \) rupees.

### Step 2: Determine the total payment for one year
The total payment for one year is Rs. 80 plus one pair of jeans, which can be expressed as:
\[ \text{Total payment for one year} = 80 + X \]

### Step 3: Calculate the monthly payment
Since the servant was supposed to serve for one year (12 months), the monthly payment can be calculated as:
\[ \text{Monthly payment} = \frac{80 + X}{12} \]

### Step 4: Calculate the total payment for 9 months
The servant worked for 9 months and received Rs. 55 plus a pair of jeans. Therefore, the total payment he received can be expressed as:
\[ \text{Total payment for 9 months} = 55 + X \]

### Step 5: Set up the equation
Since the payment for 9 months should equal the monthly payment multiplied by 9, we can set up the equation:
\[ \frac{80 + X}{12} \times 9 = 55 + X \]

### Step 6: Simplify the equation
Multiply both sides by 12 to eliminate the fraction:
\[ 9(80 + X) = 12(55 + X) \]
Expanding both sides gives:
\[ 720 + 9X = 660 + 12X \]

### Step 7: Rearrange the equation
Rearranging the equation to isolate \( X \):
\[ 720 - 660 = 12X - 9X \]
This simplifies to:
\[ 60 = 3X \]

### Step 8: Solve for \( X \)
Dividing both sides by 3 gives:
\[ X = 20 \]

### Final Answer
The price of the jeans is Rs. 20.

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