Chris windener had a servent who was determined to be paid $ 250, a wrist watch and a ration for whole year? But after 9 months Widener migrated to India and he has just paid him $270 and the ration for the 9 months. What is the cost of wrist watch?

Options

A. 20
B. 120
C. 110
D. data insufficient.

Answer

To find the cost of the wristwatch, we can break down the problem step by step.

### Step-by-Step Solution:

1. **Determine the Total Payment for the Year**:
The servant was supposed to be paid a total of $250, a wristwatch, and a ration for the whole year.

**Total Payment = $250 + Wristwatch + Ration for 12 months**

2. **Calculate the Payment for 9 Months**:
Since Chris only paid the servant for 9 months before migrating, we need to find out how much he should have paid for 9 months.

**Payment for 9 months = (9/12) * Total Payment**
- The total payment for the year is $250 + Wristwatch + Ration for 12 months.
- Therefore, the payment for 9 months can be expressed as:
\[ \text{Payment for 9 months} = \frac{3}{4} \times (250 + W + R) \]
where \( W \) is the cost of the wristwatch and \( R \) is the total cost of the ration for the year.

3. **Calculate the Amount Paid**:
Chris paid the servant $270 and provided the ration for 9 months.

**Total Paid = $270 + Ration for 9 months**
- The ration for 9 months can be expressed as:
\[ Ration for 9 months = \frac{3}{4}R \]
Thus, the total payment made by Chris can be expressed as:
\[ 270 + \frac{3}{4}R \]

4. **Set Up the Equation**:
Since the total payment for 9 months should equal the amount Chris paid, we can set up the equation:
\[ \frac{3}{4} \times (250 + W + R) = 270 + \frac{3}{4}R \]

5. **Eliminate the Ration from Both Sides**:
To simplify, we can multiply through by 4 to eliminate the fraction:
\[ 3 \times (250 + W + R) = 1080 + 3R \]
Expanding this gives:
\[ 750 + 3W + 3R = 1080 + 3R \]

6. **Solve for the Wristwatch Cost**:
Now, we can simplify the equation:
\[ 750 + 3W = 1080 \]
Subtract 750 from both sides:
\[ 3W = 330 \]
Now, divide by 3:
\[ W = 110 \]

### Conclusion:
The cost of the wristwatch is **$110**.