The ratio of the monthly incomes of Trupti, Pallavi and Komal is `141: 172 :123`, if Trupti's annual income is `₹ 3,38 400` , what is Komal's annual income ?(In some cases, monthly income is used, while in others, annual income is used.)

Options

A. `₹4,12,800`
B. `₹3,63,500`
C. `₹3,17,600`
D. `₹2,95,200`

Explanation

To find Komal's annual income based on the given ratio of monthly incomes and Trupti's annual income, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Ratio**:
The ratio of the monthly incomes of Trupti, Pallavi, and Komal is given as \( 141 : 172 : 123 \).

2. **Assign Variables to Monthly Incomes**:
Let the monthly incomes of Trupti, Pallavi, and Komal be represented as:
- Trupti's monthly income = \( 141X \)
- Pallavi's monthly income = \( 172X \)
- Komal's monthly income = \( 123X \)

3. **Convert Trupti's Annual Income to Monthly Income**:
We know that Trupti's annual income is \( ₹ 3,38,400 \). To find her monthly income, we divide her annual income by 12:
\[ \text{Trupti's monthly income} = \frac{3,38,400}{12} = ₹ 28,200 \]

4. **Set Up the Equation**:
Since Trupti's monthly income is also represented as \( 141X \), we can set up the equation:
\[ 141X = 28,200 \]

5. **Solve for X**:
To find \( X \), we divide both sides of the equation by 141:
\[ X = \frac{28,200}{141} = 200 \]

6. **Calculate Komal's Monthly Income**:
Now that we have the value of \( X \), we can find Komal's monthly income:
\[ \text{Komal's monthly income} = 123X = 123 \times 200 = ₹ 24,600 \]

7. **Convert Komal's Monthly Income to Annual Income**:
To find Komal's annual income, we multiply her monthly income by 12:
\[ \text{Komal's annual income} = 24,600 \times 12 = ₹ 2,95,200 \]

### Final Answer:
Komal's annual income is \( ₹ 2,95,200 \).

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