A man engaged a servant on the condition that he would pay him Rs90 and a turban after service of one year. He served only for nine months and received the turban and an amount of Rs 65. The price of turban is

Options

A. Rs 25
B. Rs `18.75`
C. Rs 10
D. Rs `2.50`

Answer

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

### Step 1: Define the Variables
Let the price of the turban be \( x \).

### Step 2: Calculate Total Payment for One Year
The total payment for one year (12 months) is Rs 90 plus the turban. Therefore, the total payment for one year can be expressed as:
\[ \text{Total payment for 1 year} = 90 + x \]

### Step 3: Calculate Payment for Nine Months
Since the servant worked for 9 months, we need to calculate how much he should be paid for that duration. The payment for 9 months can be calculated as:
\[ \text{Payment for 9 months} = \frac{9}{12} \times (90 + x) = \frac{3}{4} \times (90 + x) = \frac{270 + 3x}{4} \]

### Step 4: Set Up the Equation
According to the problem, after serving for 9 months, the servant received Rs 65 and the turban. Therefore, we can set up the equation:
\[ \frac{270 + 3x}{4} = 65 + x \]

### Step 5: Clear the Fraction
To eliminate the fraction, multiply both sides of the equation by 4:
\[ 270 + 3x = 4(65 + x) \]
This simplifies to:
\[ 270 + 3x = 260 + 4x \]

### Step 6: Rearrange the Equation
Now, rearranging the equation to isolate \( x \):
\[ 270 - 260 = 4x - 3x \]
This simplifies to:
\[ 10 = x \]

### Step 7: Conclusion
Thus, the price of the turban is:
\[ \boxed{10} \]