The monthly incomes of A and B are in the ratio 3 : 4 and the ratio of their monthly expenditures is 2 : 3. If each saves Rs. 4000 per month, then what is the income of B?

Options

A. A)Rs. 20000
B. B)Rs. 12000
C. C)Rs. 16000
D. D)Rs. 14000

Answer

To solve the problem, we will break it down step by step.

### Step 1: Define the Incomes and Expenditures
Let the monthly incomes of A and B be represented as:
- Income of A = 3x
- Income of B = 4x

Let the monthly expenditures of A and B be represented as:
- Expenditure of A = 2y
- Expenditure of B = 3y

### Step 2: Set Up the Savings Equation
We know that both A and B save Rs. 4000 each month. Therefore, we can write the following equations based on their incomes and expenditures:

For A:
\[ \text{Income of A} - \text{Expenditure of A} = \text{Savings of A} \]
\[ 3x - 2y = 4000 \] (Equation 1)

For B:
\[ \text{Income of B} - \text{Expenditure of B} = \text{Savings of B} \]
\[ 4x - 3y = 4000 \] (Equation 2)

### Step 3: Solve the Equations
We have two equations:
1. \( 3x - 2y = 4000 \)
2. \( 4x - 3y = 4000 \)

We can solve these equations simultaneously.

From Equation 1:
\[ 2y = 3x - 4000 \]
\[ y = \frac{3x - 4000}{2} \] (Equation 3)

Now substitute Equation 3 into Equation 2:
\[ 4x - 3\left(\frac{3x - 4000}{2}\right) = 4000 \]

Multiply through by 2 to eliminate the fraction:
\[ 8x - 3(3x - 4000) = 8000 \]
\[ 8x - 9x + 12000 = 8000 \]
\[ -x + 12000 = 8000 \]
\[ -x = 8000 - 12000 \]
\[ -x = -4000 \]
\[ x = 4000 \]

### Step 4: Find the Income of B
Now that we have the value of x, we can find the income of B:
\[ \text{Income of B} = 4x = 4 \times 4000 = 16000 \]

### Conclusion
Thus, the income of B is Rs. 16000.