Raman spends 80% of his income. If his income increases by 25% and his expenditure increases by 10%, then by what percentage do his savings increase?

Introduction / Context:
This question tests understanding of the relationship between income, expenditure and savings when both income and expenditure change by different percentages. It is not enough to look only at the changes in percentages; we must also consider how these changes affect the absolute amounts and the resulting savings. This type of question is common in topics on profit, loss and savings in aptitude tests.

Given Data / Assumptions:

• Initially, Raman spends 80% of his income.
• Therefore, initially he saves 20% of his income.
• His income then increases by 25%.
• His expenditure increases by 10%.
• We must find the percentage increase in his savings.

Concept / Approach:
Let the initial income be I. Initial expenditure is 0.80 * I, and initial saving is 0.20 * I. When income increases by 25%, new income becomes 1.25 * I. Expenditure increases by 10%, so new expenditure becomes 1.10 times the original expenditure (0.80 * I), that is 0.88 * I. New savings then equal new income minus new expenditure. After finding initial and new savings in terms of I, we compare them to determine the percentage increase in savings.

Step-by-Step Solution:
Step 1: Let initial income = I. Step 2: Initial expenditure = 80% of I = 0.80 * I. Step 3: Initial savings = income - expenditure = I - 0.80 * I = 0.20 * I. Step 4: After a 25% increase, new income = 1.25 * I. Step 5: After a 10% increase in expenditure, new expenditure = 1.10 * (0.80 * I) = 0.88 * I. Step 6: New savings = new income - new expenditure = 1.25 * I - 0.88 * I = 0.37 * I. Step 7: Initial savings were 0.20 * I and new savings are 0.37 * I. Step 8: Increase in savings = 0.37 * I - 0.20 * I = 0.17 * I. Step 9: Percentage increase in savings = (increase / original savings) * 100 = (0.17 * I / 0.20 * I) * 100. Step 10: The I cancels out, leaving (0.17 / 0.20) * 100 = 0.85 * 100 = 85%.

Verification / Alternative check:
To verify, choose a concrete value, for example I = Rs. 100. Initially, Raman spends Rs. 80 and saves Rs. 20. After the changes, new income = 125, new expenditure = 1.10 * 80 = 88, and new savings = 125 - 88 = 37. The increase in savings is 37 - 20 = 17. Percentage increase = (17 / 20) * 100 = 85%. This confirms the earlier algebraic result.

Why Other Options Are Wrong:
17 is the absolute increase (in our I = 100 example), not the percentage increase. 70% and 77% are smaller than the actual ratio of new savings to old savings. The calculations clearly show that the increase is 85% of the original saving, so only 85 is correct.

Common Pitfalls:
A frequent error is to think that since income increased by 25% and expenditure increased by 10%, savings must increase by 15%. This is wrong because savings are the difference between two quantities that are both changing. Another pitfall is to forget that the 10% increase in expenditure is on the original expenditure, not on income. Always translate the situation into explicit algebraic expressions before computing percentage changes in derived quantities like savings.

Final Answer:
Raman's savings increase by 85%.