Question

Aman spends $50%$ of his income. If income increases by $20%$ and expenses increases by $10%$, his saving will increases by:

• A. 25%
• B. 30%
• C. 35%
• D. 40%

Hint:

Using 100 as a base value simplifies almost all percentage increase/decrease problems.
It eliminates the need to work with complex fractions or variables, which minimizes the likelihood of calculation mistakes during timed tests.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question describes Aman's initial financial behavior: he spends $50%$ of his income, which means he saves the remaining $50%$.
Then, both his income and his expenses undergo a percentage increase.
We need to calculate his new income, new expenses, and the resulting new savings to find the percentage increase in his savings.

Step 2: Key Formula or Approach:
We use the fundamental accounting identity:
\[ \text{Income} = \text{Expenditure} + \text{Savings} \]
We can assume a convenient baseline value for Aman's initial income, such as 100, to make the percentage calculations straightforward.

Step 3: Detailed Explanation:
$\bullet$

Step 1: Define Initial Scenario:
Let Aman's initial Income (\(I_1\)) = 100.
Since he spends $50%$ of his income:
Initial Expenses (\(E_1\)) = \(50% \text{ of } 100 = 50\).
Initial Savings (\(S_1\)) = \(I_1 - E_1 = 100 - 50 = 50\).
$\bullet$

Step 2: Define New Scenario after Increases:
His income increases by $20%$:
New Income (\(I_2\)) = \(100 \times \left(1 + \frac{20}{100}\right) = 120\).
His expenses increase by $10%$:
New Expenses (\(E_2\)) = \(50 \times \left(1 + \frac{10}{100}\right) = 55\).
New Savings (\(S_2\)) = \(I_2 - E_2 = 120 - 55 = 65\).
$\bullet$

Step 3: Calculate the Percentage Increase in Savings:
Absolute increase in savings = \(S_2 - S_1 = 65 - 50 = 15\).
Percentage increase in savings:
\[ \text{Percentage Increase} = \left( \frac{\text{Increase in Savings}}{\text{Initial Savings}} \right) \times 100 \]
\[ \text{Percentage Increase} = \left( \frac{15}{50} \right) \times 100 \]
\[ \text{Percentage Increase} = 15 \times 2 = 30% \]
Therefore, Aman's savings will increase by $30%$.

Step 4: Final Answer:
Aman's savings will increase by $30%$.