A man spends 70% of his income and saves the rest. If his income decreases by 30% and spending decreases by 20%, then what is the percentage change in his savings?

Options

A. 66.66% decrease
B. 53.33% decrease
C. 75% increase
D. 40% decrease

Answer

To solve the problem, we will break it down into steps and calculate the man's savings before and after the changes in income and spending.

### Step 1: Calculate Initial Income and Savings
Let the man's initial income be \( I \).

- He spends 70% of his income, which is:
\[ \text{Spending} = 0.7I \]
- Therefore, his savings will be:
\[ \text{Savings} = I - \text{Spending} = I - 0.7I = 0.3I \]

### Step 2: Calculate New Income After Decrease
The man's income decreases by 30%. Thus, his new income \( I' \) is:
\[ I' = I - 0.3I = 0.7I \]

### Step 3: Calculate New Spending After Decrease
His spending decreases by 20%. The initial spending was \( 0.7I \), so the new spending \( S' \) is:
\[ S' = 0.7I - 0.2 \times 0.7I = 0.7I \times (1 - 0.2) = 0.7I \times 0.8 = 0.56I \]

### Step 4: Calculate New Savings After Changes
Now we can calculate the new savings \( S' \):
\[ S' = I' - S' = 0.7I - 0.56I = 0.14I \]

### Step 5: Calculate Percentage Change in Savings
Now we need to find the percentage change in savings. The initial savings were \( 0.3I \) and the new savings are \( 0.14I \).

The change in savings is:
\[ \text{Change in Savings} = S' - \text{Initial Savings} = 0.14I - 0.3I = -0.16I \]

To find the percentage change:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Savings}}{\text{Initial Savings}} \right) \times 100 = \left( \frac{-0.16I}{0.3I} \right) \times 100 = \left( \frac{-0.16}{0.3} \right) \times 100 \approx -53.33\% \]

### Final Answer
The percentage change in his savings is approximately **-53.33%**.

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