A person saves every year 20% of his income. If his income increases every year by 10%, then his savings increase every year by

Options

A. `10%`
B. `5%`
C. `2%`
D. `1%`

Answer

To solve the problem step by step, we can follow this approach:

### Step 1: Define the Income
Let the person's initial income be \( x \).

### Step 2: Calculate Initial Savings
The person saves 20% of his income. Therefore, his savings can be calculated as:
\[ \text{Savings} = 20\% \text{ of } x = \frac{20}{100} \times x = 0.2x \]

### Step 3: Calculate the Increased Income
The income increases by 10% every year. So, the income for the next year will be:
\[ \text{Next Year's Income} = x + 10\% \text{ of } x = x + \frac{10}{100} \times x = x + 0.1x = 1.1x \]

### Step 4: Calculate Next Year's Savings
Next, we calculate the savings for the next year based on the increased income:
\[ \text{Next Year's Savings} = 20\% \text{ of } 1.1x = \frac{20}{100} \times 1.1x = 0.22x \]

### Step 5: Calculate the Increase in Savings
Now, we find the increase in savings from this year to next year:
\[ \text{Increase in Savings} = \text{Next Year's Savings} - \text{Current Year's Savings} = 0.22x - 0.2x = 0.02x \]

### Step 6: Calculate the Percentage Increase in Savings
To find the percentage increase in savings:
\[ \text{Percentage Increase} = \left(\frac{\text{Increase in Savings}}{\text{Current Year's Savings}}\right) \times 100 = \left(\frac{0.02x}{0.2x}\right) \times 100 \]
\[ = \left(\frac{0.02}{0.2}\right) \times 100 = 0.1 \times 100 = 10\% \]

### Conclusion
Thus, the savings increase every year by **10%**.

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