Shortcut Trick
Total initial expenditure = 25% (food) + 15% (books) = 40%
Remaining income = 100% − 40% = 60%
Income left after uniform expense = (100% − 75%) of remaining income
⇒ Income left = 25% of 60% = 15%
∴ The correct answer is 15%.
Alternate Method
Given:
Expenditure on food = 25%
Expenditure on children's books = 15%
Expenditure on uniforms = 75% of the remaining income
Total = 100%
Food+Books 40%
Remaining 60%
Uniforms 45%
Left 15%
Calculations:
⇒ Total initial expenditure = 25% + 15% = 40%
⇒ Remaining income = 100% − 40% = 60%
⇒ Expenditure on uniforms = 75% of remaining income
⇒ Expenditure on uniforms = (75 ÷ 100) × 60% = 45%
⇒ Percentage of income left = Remaining income − Expenditure on uniforms
⇒ Percentage of income left = 60% − 45% = 15%
∴ The correct answer is 15%.
Additional Information
Successive Percentage Change
When calculating percentages on remaining values, multiply the successive remaining percentage parts. Formula: Final Value = Initial Value × (1 − r1/100) × (1 − r2/100).
Percentage Base Identification
Always identify the base on which the percentage is calculated. Expenditures on total income are added together first, whereas expenditures on the remaining income require updating the base before calculation.
Fractional Equivalents
Memorizing common fractions accelerates percentage calculations. For example, 25% = 1/4 and 75% = 3/4. This allows quick mental math, making tasks like computing 1/4 of 60% instantly yield 15%.