Kalyan spends 80% of his income. His income increases by 15% and his expenditure also increases by 5%. The percentage of increase in his savings is:

Correct — C. No income figure is given, so take income as 100 and the percentages become rupees.

Spends 80% → expenditure 80, savings = 100 − 80 = 20
New income = 100 × 1.15 = 115
New expenditure = 80 × 1.05 = 84
New savings = 115 − 84 = 31

Rise = 31 − 20 = 11
11⁄20 × 100 = 55% → option (c).

Why the others are wrong

• (a)
  20% — 20% is the share of income he saves, not the growth in savings. Savings went from 20 to 31, and the question asks about that jump.
• (b)
  50% — 50% needs savings of 30, i.e. a rise of 10. That is 15 − 5 with the 5% taken on income; the 5% belongs to the expenditure of 80, and 5% of 80 is 4, not 5.
• (d)
  40% — 40% needs a rise of 8, which is 15% of 80 minus 5% of 80 — both changes applied to the expenditure base. The 15% acts on income.

Savings are a difference, so a percentage change in savings is not the difference of the two percentage changes.

Income rises on a base of 100 and expenditure on a base of 80, so the same-looking percentages move very different amounts of money: +15 against +4.

Because only ratios are asked for, any starting income works. Taking 100 makes the expenditure 80 and the savings 20 without a single fraction, and the final answer 11⁄20 is read straight off.

Key facts

• Savings = income − expenditure, so a change in savings is a change in a difference.
• A 15% rise on an income of 100 adds 15, while a 5% rise on an expenditure of 80 adds only 4.
• Percentage rise in savings = (new savings − old savings) ÷ old savings × 100.
• Here savings move 20 → 31, a rise of 11 on a base of 20.

Common traps

• Subtracting 15% − 5% and calling the result the rise in savings
• Answering with the savings rate, 20%, instead of its increase
• Taking 5% of income rather than 5% of expenditure

No directly related past PYQ was found.