A man spends 80% of his income and saves the rest. If his income and spending both increases by 10%, then what is the percentage change in his savings?

Options

A. a. 10% increase
B. b. 5% decrease
C. c. 5% increase
D. d. 15% decrease

Answer

To solve the problem step by step, let's define the variables and calculate the savings before and after the increase in income and spending.

### Step 1: Define the initial income and savings
Let the man's initial income be \( I \). According to the problem, he spends 80% of his income. Therefore, his spending is:
\[ \text{Spending} = 0.8I \]
His savings, which is the remaining part of his income, can be calculated as:
\[ \text{Savings} = I - \text{Spending} = I - 0.8I = 0.2I \]

### Step 2: Calculate the new income and spending after a 10% increase
If both his income and spending increase by 10%, the new income \( I' \) becomes:
\[ I' = I + 0.1I = 1.1I \]
The new spending \( S' \) is:
\[ S' = 0.8I + 0.1 \times 0.8I = 0.8I + 0.08I = 0.88I \]

### Step 3: Calculate the new savings
Now, we can find the new savings \( S' \):
\[ S' = I' - S' = 1.1I - 0.88I = 0.22I \]

### Step 4: Determine the change in savings
The initial savings were \( 0.2I \) and the new savings are \( 0.22I \). The change in savings is:
\[ \text{Change in savings} = S' - \text{Initial Savings} = 0.22I - 0.2I = 0.02I \]

### Step 5: Calculate the percentage change in savings
To find the percentage change in savings, we use the formula:
\[ \text{Percentage Change} = \left( \frac{\text{Change in savings}}{\text{Initial Savings}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage Change} = \left( \frac{0.02I}{0.2I} \right) \times 100 = \left( \frac{0.02}{0.2} \right) \times 100 = 10\% \]

### Conclusion
Thus, the percentage change in his savings is **10%**.

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