The respective ratio of Sita's, Riya's and Kunal's monthly incomes is 84 : 76 : 89. If Riya's annual income is X 456000, then what is the sum of Sita's and Kunal's annual incomes? (In some cases monthly income and in some cases annual income is used.)

Options

A. X 195000
B. X 983500
C. X 1130000
D. X 1038000

Answer

To solve the problem step by step, we will follow the given ratios and the information about Riya's annual income.

### Step 1: Understand the Ratios
The monthly incomes of Sita, Riya, and Kunal are in the ratio of 84:76:89. We can express their incomes in terms of a constant \( K \):
- Sita's monthly income = \( 84K \)
- Riya's monthly income = \( 76K \)
- Kunal's monthly income = \( 89K \)

### Step 2: Find Riya's Monthly Income
Given that Riya's annual income is \( 456,000 \), we first need to find her monthly income:
\[ \text{Riya's monthly income} = \frac{456,000}{12} = 38,000 \]

### Step 3: Set Up the Equation
Since Riya's monthly income is also represented as \( 76K \), we can set up the equation:
\[ 76K = 38,000 \]

### Step 4: Solve for \( K \)
To find the value of \( K \), we divide both sides of the equation by 76:
\[ K = \frac{38,000}{76} = 500 \]

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

### Step 6: Find the Sum of Sita's and Kunal's Monthly Incomes
Now, we can find the sum of Sita's and Kunal's monthly incomes:
\[ \text{Sum of Sita's and Kunal's monthly incomes} = 42,000 + 44,500 = 86,500 \]

### Step 7: Convert Monthly Income to Annual Income
To find the annual income, we multiply the sum of their monthly incomes by 12:
\[ \text{Sum of Sita's and Kunal's annual incomes} = 86,500 \times 12 = 1,038,000 \]

### Final Answer
The sum of Sita's and Kunal's annual incomes is \( 1,038,000 \).

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