Last year, Vivek saved 10% of his annual income. This year, he earned 5% more than last year and saved 12% of his annual income. The amount saved this year was what percentage of the amount saved last year?

Introduction / Context:
This question tests percentage comparison between two years, focusing on how a change in income and a change in saving percentage together affect the amount saved. Such problems are common in aptitude exams because they combine basic percentage increase with percentage of a quantity, and then ask you to express one amount as a percentage of another.

Given Data / Assumptions:

• Last year, Vivek saved 10% of his annual income.
• This year, his annual income increased by 5% compared to last year.
• This year, he saved 12% of his annual income.
• We assume income is positive and there are no other changes.
• We need the amount saved this year as a percentage of the amount saved last year.

Concept / Approach:
The key idea is to use a convenient assumed value for last year's income, convert the given percentages to actual amounts, and then compare the new saving with the old saving. Because everything is in percentages, we can assume last year's income as 100 units (or any other value). Then we apply the income increase and the saving percentages. Finally, we compute the ratio: (saving this year) / (saving last year) and convert this ratio into a percentage.

Step-by-Step Solution:
Step 1: Assume last year's income = I. Step 2: Last year's saving = 10% of I = 0.10 * I. Step 3: This year's income increased by 5%, so new income = 1.05 * I. Step 4: This year, Vivek saves 12% of his new income, so saving this year = 0.12 * (1.05 * I) = 0.126 * I. Step 5: Now compare the two savings. Ratio = (saving this year) / (saving last year) = (0.126 * I) / (0.10 * I). Step 6: The I cancels out, so ratio = 0.126 / 0.10 = 1.26. Step 7: A ratio of 1.26 means the new saving is 1.26 times the old saving, that is 126% of the previous amount.

Verification / Alternative check:
Take I = 100 as a concrete number. Then last year he saved 10% of 100 = 10 units. This year income is 5% more, so 105, and he saves 12% of that, that is 12.6 units. Now express 12.6 as a percentage of 10: (12.6 / 10) * 100 = 126%. This matches our earlier result, so the calculation is consistent.

Why Other Options Are Wrong:
87% would indicate that this year's saving is less than last year's, which is impossible because both income and saving percentage increased.
98% suggests almost no change, which again contradicts the combined effect of 5% higher income and a higher saving rate.
138% would mean the saving increased a lot more than it actually did; the exact ratio is 1.26, not 1.38.

Common Pitfalls:
Many learners mistakenly add percentages directly (for example, 10% saving becoming 12% saving and income rising by 5%) and try to combine them incorrectly. Some also forget that a 5% increase in income affects the base on which the saving percentage is calculated. Others simply compare 12% with 10% and say 120% instead of carefully computing the effect of the higher base income. Always translate the words into algebra or numbers systematically.

Final Answer:
The amount saved this year is 126% of the amount saved last year.