The respective ratio between pooja, prathana, and falguni monthly income is 53:70:57. If prathana annual income is Rs.4,20,000, what is the pooja and falguni annual incomes?

Options

A. a. Rs.5,92,500
B. b. Rs. 6,83,500
C. c. Rs. 6,60,000
D. d. Rs. 7,79,200

Answer

To solve the problem step by step, we will follow the given information and use the ratios to find the required incomes.

### Step 1: Understand the Ratios
The monthly income ratio of Pooja, Prathana, and Falguni is given as:
- Pooja : Prathana : Falguni = 53 : 70 : 57

### Step 2: Find Prathana's Monthly Income
We know Prathana's annual income is Rs. 4,20,000. To find her monthly income, we divide her annual income by 12 (the number of months in a year):
\[ \text{Prathana's Monthly Income} = \frac{4,20,000}{12} = 35,000 \]

### Step 3: Set Up the Ratio
From the ratio, we know that Prathana's income corresponds to 70 parts. Therefore, we can set up the equation:
\[ 70 \text{ parts} = 35,000 \]

### Step 4: Calculate the Value of One Part
To find the value of one part, we divide Prathana's monthly income by 70:
\[ \text{Value of One Part} = \frac{35,000}{70} = 500 \]

### Step 5: Calculate Pooja's Monthly Income
Pooja's income corresponds to 53 parts. Therefore, we can calculate Pooja's monthly income:
\[ \text{Pooja's Monthly Income} = 53 \times 500 = 26,500 \]

### Step 6: Calculate Falguni's Monthly Income
Falguni's income corresponds to 57 parts. Therefore, we can calculate Falguni's monthly income:
\[ \text{Falguni's Monthly Income} = 57 \times 500 = 28,500 \]

### Step 7: Calculate Annual Incomes
To find the annual incomes, we multiply the monthly incomes by 12:
- Pooja's Annual Income:
\[ \text{Pooja's Annual Income} = 26,500 \times 12 = 3,18,000 \]
- Falguni's Annual Income:
\[ \text{Falguni's Annual Income} = 28,500 \times 12 = 3,42,000 \]

### Final Results
- Pooja's Annual Income = Rs. 3,18,000
- Falguni's Annual Income = Rs. 3,42,000

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