Bina's monthly income is 90% of Anita's monthly income . The total ot both their monthly incomes is Mr. Sen's montly income. Mr. Sen's annual income is 7,75,200. What is Bina 's montly income ?

Options

A. Rs. 34,000
B. Rs. 36,000
C. Rs. 30,600
D. Rs. 30,000

Explanation

To find Bina's monthly income, we will follow these steps:

### Step 1: Determine Mr. Sen's Monthly Income
Mr. Sen's annual income is given as 7,75,200. To find his monthly income, we divide the annual income by 12 (the number of months in a year).

\[ \text{Mr. Sen's Monthly Income} = \frac{7,75,200}{12} \]

Calculating this:

\[ \text{Mr. Sen's Monthly Income} = 64,600 \]

### Step 2: Set Up the Relationship Between Bina's and Anita's Income
Let Anita's monthly income be \( X \). According to the problem, Bina's monthly income is 90% of Anita's monthly income. Therefore, we can express Bina's income as:

\[ \text{Bina's Monthly Income} = \frac{90}{100} \times X = \frac{9}{10} X \]

### Step 3: Write the Equation for Total Income
The total monthly income of Bina and Anita is equal to Mr. Sen's monthly income. Thus, we can write the equation:

\[ \text{Bina's Monthly Income} + \text{Anita's Monthly Income} = \text{Mr. Sen's Monthly Income} \]

Substituting the values we have:

\[ \frac{9}{10} X + X = 64,600 \]

### Step 4: Combine Like Terms
To combine the terms on the left side, we need a common denominator:

\[ \frac{9X}{10} + \frac{10X}{10} = \frac{19X}{10} \]

So the equation becomes:

\[ \frac{19X}{10} = 64,600 \]

### Step 5: Solve for \( X \)
To isolate \( X \), we multiply both sides by 10:

\[ 19X = 64,600 \times 10 \]

Calculating this gives:

\[ 19X = 646,000 \]

Now, divide both sides by 19:

\[ X = \frac{646,000}{19} \]

Calculating this gives:

\[ X = 34,000 \]

### Step 6: Calculate Bina's Monthly Income
Now that we have \( X \) (Anita's monthly income), we can find Bina's monthly income:

\[ \text{Bina's Monthly Income} = \frac{9}{10} \times 34,000 \]

Calculating this gives:

\[ \text{Bina's Monthly Income} = 30,600 \]

### Final Answer
Bina's monthly income is **30,600**.

---