Step 1: Understanding the Concept:
This problem explores the relationship between three variables: Income, Expenditure (expenses), and Savings.
The fundamental relationship is: \( \text{Income} = \text{Expenditure} + \text{Savings} \).
Changes in percentages can be tricky if we use variables alone.
In such cases, assuming a starting base value (like 100) for income makes the percentage transformations much more intuitive and less prone to calculation errors.
Step 2: Key Formula or Approach:
Initial Scenario: Set Income = 100.
Update each component (Income and Expenditure) based on the percentage growth specified in the problem.
Calculate the resulting change in Savings.
Step 3: Detailed Explanation:
Let's define the initial state:
Initial Income (\( I_1 \)) = 100 units.
Aman spends 50%, so Initial Expenditure (\( E_1 \)) = 50.
Initial Savings (\( S_1 \)) = Income \( - \) Expenditure = \( 100 - 50 = 50 \).
Now, calculate the new state after increases:
Income increases by 20%: New Income (\( I_2 \)) = \( 100 + 20 = 120 \).
Expenditure increases by 10%: New Expenditure (\( E_2 \)) = \( 50 + (10% \text{ of } 50) = 50 + 5 = 55 \).
Now, calculate the new Savings:
New Savings (\( S_2 \)) = \( 120 - 55 = 65 \).
Finally, calculate the percentage increase in savings:
Absolute Increase = \( S_2 - S_1 = 65 - 50 = 15 \).
\[ \text{Percentage Increase} = \left( \frac{\text{Increase}}{\text{Original value}} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{15}{50} \right) \times 100 \]
\[ \text{Percentage Increase} = 0.3 \times 100 = 30% \]
Step 4: Final Answer:
Aman’s savings will increase by 30%.