My salary is Rs. 12,345 per month. The salary of my brother is 10% greater than that of mine. The salary of my only sister is 9.09% greater than my only brother. The salary of my wife is `56(12)/(23)%` less than the total salary of my brother and sister together, then the salary of my wife is :

Options

A. greater than my sister's salary
B. `33(11)/(23)%` less than my sister's salary
C. equal to my salary
D. `44(11)/(23)%` greater than my own salary

Answer

To solve the problem step by step, we will calculate the salaries of the brother, sister, and wife based on the given information.

### Step 1: Calculate Brother's Salary
- My salary = Rs. 12,345
- Brother's salary is 10% greater than mine.

\[ \text{Brother's Salary} = \text{My Salary} + 10\% \text{ of My Salary} \]

\[ \text{Brother's Salary} = 12,345 + \left(\frac{10}{100} \times 12,345\right) \]

\[ \text{Brother's Salary} = 12,345 + 1,234.5 = 13,579.5 \]

### Step 2: Calculate Sister's Salary
- Sister's salary is 9.09% greater than the brother's salary.

\[ \text{Sister's Salary} = \text{Brother's Salary} + 9.09\% \text{ of Brother's Salary} \]

\[ \text{Sister's Salary} = 13,579.5 + \left(\frac{9.09}{100} \times 13,579.5\right) \]

\[ \text{Sister's Salary} = 13,579.5 + 1,234.5 = 14,814.88 \]

### Step 3: Calculate Total Salary of Brother and Sister
- Total Salary = Brother's Salary + Sister's Salary

\[ \text{Total Salary} = 13,579.5 + 14,814.88 = 28,394.38 \]

### Step 4: Calculate Wife's Salary
- Wife's salary is \(56 \frac{12}{23}\%\) less than the total salary of brother and sister.

First, convert \(56 \frac{12}{23}\%\) to a decimal:

\[ 56 \frac{12}{23} = 56 + \frac{12}{23} = \frac{56 \times 23 + 12}{23} = \frac{1288 + 12}{23} = \frac{1300}{23} \approx 56.52\% \]

- Thus, the percentage of the total salary that the wife receives is:

\[ 100\% - 56.52\% = 43.48\% \]

- Now calculate the wife’s salary:

\[ \text{Wife's Salary} = 43.48\% \text{ of Total Salary} \]

\[ \text{Wife's Salary} = \left(\frac{43.48}{100} \times 28,394.38\right) \]

\[ \text{Wife's Salary} \approx 12,345.00 \]

### Final Answer
The salary of my wife is approximately Rs. 12,345.

---