The ratio of Sita's , Riya and Kunal's monthly income is `84 :76:89`.If Riya annual income is `₹ 4,56,000`, what is the sum of Sita's and Kunal's annual incomes? (In some cases monthly income is used while in others annual income is used.)

Options

A. `₹11,95,000`
B. `₹9,83,50`
C. `₹11,30,000`
D. `₹ 10,38,000`

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given ratio and Riya's annual income
The ratio of Sita's, Riya's, and Kunal's monthly incomes is given as \(84 : 76 : 89\). Riya's annual income is given as ₹4,56,000.

### Step 2: Calculate Riya's monthly income
To find Riya's monthly income, we divide her annual income by 12 (since there are 12 months in a year):
\[ \text{Riya's monthly income} = \frac{4,56,000}{12} = 38,000 \]

### Step 3: Set up the equations based on the ratio
Let the monthly incomes of Sita, Riya, and Kunal be represented as:
- Sita's monthly income = \(84x\)
- Riya's monthly income = \(76x\)
- Kunal's monthly income = \(89x\)

From the previous step, we know Riya's monthly income is ₹38,000, so we can set up the equation:
\[ 76x = 38,000 \]

### Step 4: Solve for \(x\)
To find \(x\), we rearrange the equation:
\[ x = \frac{38,000}{76} = 500 \]

### Step 5: Calculate Sita's and Kunal's monthly incomes
Now that we have \(x\), we can calculate Sita's and Kunal's monthly incomes:
- Sita's monthly income = \(84x = 84 \times 500 = 42,000\)
- Kunal's monthly income = \(89x = 89 \times 500 = 44,500\)

### Step 6: Calculate Sita's and Kunal's annual incomes
To find their annual incomes, we multiply their monthly incomes by 12:
- Sita's annual income = \(42,000 \times 12 = 5,04,000\)
- Kunal's annual income = \(44,500 \times 12 = 5,34,000\)

### Step 7: Calculate the sum of Sita's and Kunal's annual incomes
Finally, we find the sum of Sita's and Kunal's annual incomes:
\[ \text{Sum} = 5,04,000 + 5,34,000 = 10,38,000 \]

### Final Answer
The sum of Sita's and Kunal's annual incomes is **₹10,38,000**.

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