The monthly incomes of A and B are in the ratio 3 : 2 , and the monthly expenditures of the two are in the ratio 4 : 3","Column B"),("Saving of A",,"Saving of B"):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we will follow these steps:

### 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 = 2x

Let the monthly expenditures of A and B be represented as:
- Expenditure of A = 4y
- Expenditure of B = 3y

### Step 2: Calculate the savings of A and B
Savings can be calculated using the formula:
\[ \text{Savings} = \text{Income} - \text{Expenditure} \]

For A:
\[ \text{Savings of A} = \text{Income of A} - \text{Expenditure of A} \]
\[ \text{Savings of A} = 3x - 4y \]

For B:
\[ \text{Savings of B} = \text{Income of B} - \text{Expenditure of B} \]
\[ \text{Savings of B} = 2x - 3y \]

### Step 3: Compare the savings of A and B
To determine which saving is greater, we will compare:
\[ \text{Savings of A} - \text{Savings of B} \]
\[ = (3x - 4y) - (2x - 3y) \]
\[ = 3x - 4y - 2x + 3y \]
\[ = (3x - 2x) + (-4y + 3y) \]
\[ = x - y \]

### Step 4: Analyze the result
The comparison gives us:
\[ x - y > 0 \]
This implies:
\[ x > y \]

### Conclusion
Since \( x > y \), it follows that:
\[ \text{Savings of A} > \text{Savings of B} \]

Thus, the answer is that the savings of A are greater than the savings of B.

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