The ratio of incomes of Pankaj and Gauri is `3 : 5` and the ratio of their expenditures is `2 : 3`. Who does save more? (You have to assume that no one takes any loan from anywhere)

Options

A. Pankaj
B. Gauri
C. Both save equally
D. Depends upon the incomes of Pankaj and Gauri

Answer

To determine who saves more between Pankaj and Gauri, we will follow these steps:

### Step 1: Define the Incomes
Let the incomes of Pankaj and Gauri be represented as:
- Income of Pankaj = 3x
- Income of Gauri = 5x

### Step 2: Define the Expenditures
Let the expenditures of Pankaj and Gauri be represented as:
- Expenditure of Pankaj = 2y
- Expenditure of Gauri = 3y

### Step 3: Calculate Savings
Savings can be calculated by subtracting expenditure from income. Therefore:
- Savings of Pankaj = Income of Pankaj - Expenditure of Pankaj
\[ \text{Savings of Pankaj} = 3x - 2y \]
- Savings of Gauri = Income of Gauri - Expenditure of Gauri
\[ \text{Savings of Gauri} = 5x - 3y \]

### Step 4: Compare Savings
To find out who saves more, we will compare the savings of Pankaj and Gauri:
We need to compare \(3x - 2y\) and \(5x - 3y\).

### Step 5: Set up the Inequality
To compare the two savings:
\[ 3x - 2y \quad \text{vs} \quad 5x - 3y \]
We can rearrange this to:
\[ 3x - 2y < 5x - 3y \]
This simplifies to:
\[ y < 2x \]

### Step 6: Conclusion
Since \(y < 2x\), it indicates that Gauri saves more than Pankaj. Therefore, Gauri saves more.