The ratio of the monthly incomes of Sneha, Tina and Akruti is ` 95: 110 : 116`, if Sneha's annual incomes is ` ₹ 3,42,000`, what is Akruti annual income ?

Options

A. `₹3,96,9000`
B. `₹5,63,500`
C. `₹4,17,600`
D. `₹3,88,000`

Explanation

To solve the problem step by step, we will follow the given information and use the ratio of the monthly incomes of Sneha, Tina, and Akruti.

### Step 1: Understand the ratio of incomes
The ratio of the monthly incomes of Sneha, Tina, and Akruti is given as:
\[ \text{Sneha : Tina : Akruti} = 95 : 110 : 116 \]

### Step 2: Let the monthly incomes be expressed in terms of a variable
Let the monthly incomes of Sneha, Tina, and Akruti be represented as:
- Sneha's monthly income = \( 95x \)
- Tina's monthly income = \( 110x \)
- Akruti's monthly income = \( 116x \)

### Step 3: Calculate Sneha's monthly income from her annual income
We know that Sneha's annual income is ₹ 3,42,000. To find her monthly income, we divide her annual income by 12:
\[ \text{Sneha's monthly income} = \frac{3,42,000}{12} = 28,500 \]

### Step 4: Set up the equation to find x
Since Sneha's monthly income can also be expressed as \( 95x \), we can set up the equation:
\[ 95x = 28,500 \]

### Step 5: Solve for x
To find the value of \( x \), we rearrange the equation:
\[ x = \frac{28,500}{95} \]
Calculating this gives:
\[ x = 300 \]

### Step 6: Calculate Akruti's monthly income
Now that we have the value of \( x \), we can find Akruti's monthly income:
\[ \text{Akruti's monthly income} = 116x = 116 \times 300 = 34,800 \]

### Step 7: Calculate Akruti's annual income
To find Akruti's annual income, we multiply her monthly income by 12:
\[ \text{Akruti's annual income} = 34,800 \times 12 = 4,17,600 \]

### Final Answer
Akruti's annual income is ₹ 4,17,600.

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