A person spends `87.5%` of his income. His income increases by `59%` and expenditure increases by `67%` . Find his percentage increas or decrease in savings

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine Initial Income and Expenditure
Assume the initial income of the person is \( I = 1000 \) (for simplicity). Given that the person spends \( 87.5\% \) of his income, we can calculate the initial expenditure \( E \).

\[ E = 87.5\% \text{ of } I = 0.875 \times 1000 = 875 \]

### Step 2: Calculate Initial Savings
Savings \( S \) can be calculated as:

\[ S = I - E = 1000 - 875 = 125 \]

### Step 3: Calculate New Income After Increase
The income increases by \( 59\% \). Therefore, the new income \( I' \) is:

\[ I' = I + (59\% \text{ of } I) = 1000 + 0.59 \times 1000 = 1000 + 590 = 1590 \]

### Step 4: Calculate New Expenditure After Increase
The expenditure increases by \( 67\% \). We first calculate the increase in expenditure:

\[ \text{Increase in } E = 67\% \text{ of } E = 0.67 \times 875 = 586.25 \]

Now, we can find the new expenditure \( E' \):

\[ E' = E + \text{Increase in } E = 875 + 586.25 = 1461.25 \]

### Step 5: Calculate New Savings
Now, we can calculate the new savings \( S' \):

\[ S' = I' - E' = 1590 - 1461.25 = 128.75 \]

### Step 6: Calculate Change in Savings
To find the change in savings, we subtract the initial savings from the new savings:

\[ \text{Change in Savings} = S' - S = 128.75 - 125 = 3.75 \]

### Step 7: Calculate Percentage Change in Savings
Finally, we calculate the percentage change in savings:

\[ \text{Percentage Change} = \left( \frac{\text{Change in Savings}}{S} \right) \times 100 = \left( \frac{3.75}{125} \right) \times 100 \]

Calculating that gives:

\[ \text{Percentage Change} = 3\% \]

### Final Answer
The percentage increase in savings is \( 3\% \).

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