My salary is ₹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 that my only brother . The salary of my wife is `56 12/23%` less than the total salary of my brother and sister together, then my sister's 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, let's break it down into manageable parts.

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

**Calculation:**
- 10% of my salary = 10/100 * 12,345 = ₹1,234.50
- My brother's salary = My salary + 10% of my salary
- My brother's salary = ₹12,345 + ₹1,234.50 = ₹13,579.50

### Step 2: Calculate My Sister's Salary
My sister's salary is 9.09% greater than my brother's salary.

**Calculation:**
- 9.09% of my brother's salary = 9.09/100 * 13,579.50 = ₹1,233.77 (approximately)
- My sister's salary = My brother's salary + 9.09% of my brother's salary
- My sister's salary = ₹13,579.50 + ₹1,233.77 = ₹14,813.27 (approximately)

### Step 3: Calculate the Total Salary of My Brother and Sister
Now, we need to find the total salary of my brother and sister together.

**Calculation:**
- Total salary = My brother's salary + My sister's salary
- Total salary = ₹13,579.50 + ₹14,813.27 = ₹28,392.77 (approximately)

### Step 4: Calculate My Wife's Salary
My wife's salary is 56 12/23% less than the total salary of my brother and sister together.

**Convert 56 12/23% to a decimal:**
- 56 12/23% = 56 + (12/23) = 56.5217% (approximately)
- In decimal form = 56.5217/100 = 0.565217

**Calculation:**
- My wife's salary = Total salary - (56.5217% of Total salary)
- My wife's salary = Total salary * (1 - 0.565217)
- My wife's salary = ₹28,392.77 * (1 - 0.565217) = ₹28,392.77 * 0.434783 = ₹12,344.66 (approximately)

### Step 5: Compare My Wife's Salary to My Sister's Salary
Now, we need to find out if my wife's salary is greater than, less than, or equal to my sister's salary.

**Comparison:**
- My sister's salary = ₹14,813.27 (approximately)
- My wife's salary = ₹12,344.66 (approximately)

### Conclusion
My wife's salary is less than my sister's salary.