A man spends 35% of his income on food, 25% on children's education and 80% of the remaining on house rent. What percent of his income he is left with?

### Concept & Logic When multiple expenditures are made from the primary total income without the keyword "remaining" between them, they must be added together to find the first total deduction. Subsequent percentages applied to the "remaining" pool act as a successive deduction. ### Step-by-Step Solution * Let the man's total income be $100\%$. * **First block of expenditures:** He spends $35\%$ on food and $25\%$ on education from his total income. $$\text{Total initial spend} = 35\% + 25\% = 60\%$$ * **Remaining income:** $$\text{Remainder} = 100\% - 60\% = 40\%$$ * **Second block of expenditures:** He spends $80\%$ of this *remaining* amount on house rent. $$\text{Rent} = 80\% \text{ of } 40\% = 0.80 \times 40\% = 32\%$$ * **Final remaining percentage:** $$\text{Left with} = 40\% (\text{Remainder}) - 32\% (\text{Rent}) = 8\%$$ ### Exam Strategy & Shortcut Use a quick logical tree. Total ($100$) $\rightarrow$ Spend ($60$) $\rightarrow$ Remaining ($40$). If he spends $80\%$ of the remainder on rent, he must *save* $20\%$ of that remainder. Savings = $20\% \text{ of } 40\%$. $0.2 \times 40 = 8\%$. This bypasses calculating the exact rent amount entirely. ### Common Pitfall Students often subtract all the percentages linearly: $100 - 35 - 25 - 80$, which results in a negative number and confusion. "80% of the remaining" means the base for the 80% is the leftover amount, not the original 100. ### Final Answer **Therefore, the correct answer is 8%.**