The incomes of A and B are in the ratio 6 : 11. The ratio of their expenditures is 1 : 2. If A and B save Rs. 9,000 and Rs. 11,500, respectively, then the expenditure of B is:

Options

A. Rs. 55,500
B. Rs. 54,900
C. Rs. 55,800
D. Rs. 60,000

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Define the variables for incomes
Let the incomes of A and B be represented as:
- Income of A = 6X
- Income of B = 11X

### Step 2: Define the variables for expenditures
Let the expenditures of A and B be represented as:
- Expenditure of A = Y
- Expenditure of B = 2Y

### Step 3: Write the equations for savings
From the problem, we know the savings of A and B:
- Savings of A = Income of A - Expenditure of A = 6X - Y = 9,000
- Savings of B = Income of B - Expenditure of B = 11X - 2Y = 11,500

### Step 4: Set up the equations
From the savings information, we can set up the following equations:
1. \( 6X - Y = 9,000 \) (Equation 1)
2. \( 11X - 2Y = 11,500 \) (Equation 2)

### Step 5: Solve for Y in terms of X from Equation 1
Rearranging Equation 1 gives:
\[ Y = 6X - 9,000 \]

### Step 6: Substitute Y in Equation 2
Substituting the expression for Y into Equation 2:
\[ 11X - 2(6X - 9,000) = 11,500 \]
\[ 11X - 12X + 18,000 = 11,500 \]
\[ -X + 18,000 = 11,500 \]

### Step 7: Solve for X
Rearranging gives:
\[ -X = 11,500 - 18,000 \]
\[ -X = -6,500 \]
\[ X = 6,500 \]

### Step 8: Find the value of Y
Now substitute X back into the equation for Y:
\[ Y = 6(6,500) - 9,000 \]
\[ Y = 39,000 - 9,000 \]
\[ Y = 30,000 \]

### Step 9: Calculate the expenditure of B
The expenditure of B is:
\[ Expenditure of B = 2Y = 2(30,000) = 60,000 \]

### Final Answer
The expenditure of B is Rs. 60,000.

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