Calculating Savings Percentage Increase

This problem involves calculating the percentage change in savings based on changes in income and expenditure.

Step-by-Step Solution

1. Define Initial Variables:
   • Let the initial income be $ I $.
   • The man spends 80% of his income, so initial expenditure $ E = 0.80 \times I $.
   • Initial savings $ S = I - E = I - (0.80 \times I) = 0.20 \times I $.
2. Define New Variables:
   • The income increased by 25%, so the new income is $ I' = I + (0.25 \times I) = 1.25 \times I $.
   • The expenditure remains the same, so the new expenditure is $ E' = E = 0.80 \times I $.
   • The new savings are $ S' = I' - E' = (1.25 \times I) - (0.80 \times I) = 0.45 \times I $.
3. Calculate Percentage Increase in Savings:
   • The formula for percentage increase is $ \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100 $.
   • Percentage increase in savings = $ \frac{S' - S}{S} \times 100 $.
   • Substitute the values: $ \frac{(0.45 \times I) - (0.20 \times I)}{0.20 \times I} \times 100 $.
   • Simplify the expression: $ \frac{0.25 \times I}{0.20 \times I} \times 100 $.
   • Cancel out $ I $: $ \frac{0.25}{0.20} \times 100 $.
   • Calculate the final value: $ 1.25 \times 100 = 125\% $.

Therefore, his savings have increased by 125%.