A man spends 35% of his income on food and 25% of his income on his children's education. He then spends 80% of the remaining income on house rent. What percentage of his original income is left after all these expenditures?

Introduction / Context:
This is a multi-step percentage problem involving successive expenditures from an initial income. The man spends fixed percentages of his income on different expense categories: food, children's education and then house rent from the remaining amount. We must compute the percentage of his original income that remains after all these expenses. The question tests understanding of how sequential percentage deductions affect the remaining amount.

Given Data / Assumptions:
- Let the man's total income be I (we can imagine I = 100% for percentage calculations).- 35% of income is spent on food.- 25% of income is spent on children's education.- After these two expenses, from the remaining income, 80% is spent on house rent.- We must find what percentage of the original income I remains unspent.

Concept / Approach:
The approach is to apply each expenditure step sequentially to the income, always being careful to distinguish between percentages of the original income and percentages of the remaining income. First we subtract the percentages spent on food and education directly from the total. Then we calculate the remaining amount and apply the 80% rent expenditure to that remainder. Finally, we express the leftover amount as a percentage of the original income.

Step-by-Step Solution:
Step 1: Let the original income be 100 units (representing 100%).Step 2: Food expense = 35% of income = 35 units.Step 3: Education expense = 25% of income = 25 units.Step 4: Total spent on food and education = 35 + 25 = 60 units.Step 5: Remaining income after food and education = 100 - 60 = 40 units.Step 6: From this remaining 40 units, 80% is spent on house rent.Step 7: House rent = 80% of 40 = (80 / 100) * 40 = 32 units.Step 8: Remaining income after house rent = 40 - 32 = 8 units.Step 9: Since we started with 100 units representing 100%, the remaining 8 units represent 8% of the original income.

Verification / Alternative check:
We can verify by converting each step back to actual percentages of the original income I.Remaining income after food and education = 40% of I.House rent = 80% of the remaining 40% of I = 0.80 * 0.40 * I = 0.32I or 32% of I.Total spent overall = 35% + 25% + 32% = 92% of I.Thus, remaining income = 100% - 92% = 8% of I.This matches the 8 units out of 100 units from the earlier computation.

Why Other Options Are Wrong:
- 6 %: Too low; it would mean spending 94% of income, which is not consistent with the calculated expenses.- 10 %: Would require overall spending of 90%, not the 92% we deduced from the given data.- 12 %: This would imply only 88% spent; again, inconsistent with aggregated expenses of 35%, 25% and 32%.

Common Pitfalls:
- Adding 35%, 25% and 80% directly without realizing that 80% applies to the remaining 40%, not the original 100%.- Applying 80% to the total income instead of to the remaining 40%.- Miscomputing the remaining percentage after the first two expenses.- Confusing absolute units (for example, rupees) with percentage units while doing mental calculations.

Final Answer:
The man is left with 8% of his original income.