Practice Questions
Concept Explanation
When two or more percentage changes are applied one after another, multiply the successive multipliers — do not add the percentages.
Net Multiplier Formula
If changes are +a% and −b%, net multiplier = (1 + a/100)(1 − b/100).
Classic Placement Result
+20% then −20% on the same base gives net change = −4%, not 0%. Final = 0.8 × 1.2 = 0.96 of original.
Net Percentage Change
Net % = (Final − Original)/Original × 100, or (multiplier − 1) × 100.
Three Successive Changes
Multiply all factors: +10%, +20%, −5% → 1.1 × 1.2 × 0.95 = 1.254 → net +25.4%.
| Change 1 | Change 2 | Net Effect |
|---|---|---|
| +10% | −10% | −1% |
| +20% | −20% | −4% |
| +25% | −25% | −6.25% |
| +10% | +20% | +32% |
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Q1 Easy
A number is increased by 20% and then decreased by 20%. What is the net percentage change?
ExplanationNet multiplier = 1.2 × 0.8 = 0.96. Net change = 4% decrease. -
Q2 Easy
A number is increased by 10% and then decreased by 10%. What is the net change?
ExplanationNet multiplier = 1.1 × 0.9 = 0.99. Net change = 1% decrease. -
Q3 Medium
The price of an article is first increased by 25% and then decreased by 20%. What is the net percentage change?
ExplanationNet multiplier = 1.25 × 0.8 = 1.0. There is no net change. -
Q4 Medium
A salary of Rs. 20,000 is increased by 10% and then by another 20%. What is the final salary?
ExplanationFinal = 20,000 × 1.1 × 1.2 = 20,000 × 1.32 = Rs. 26,400. -
Q5 Easy
A number is decreased by 10% and then increased by 10%. The net change is:
Explanation0.9 × 1.1 = 0.99 → 1% decrease. -
Q6 Medium
An item costing Rs. 500 undergoes a 20% increase followed by a 10% decrease. What is the final price?
ExplanationFinal = 500 × 1.2 × 0.9 = 500 × 1.08 = Rs. 540. -
Q7 Medium
Successive increases of 10% and 20% are equivalent to a single increase of:
ExplanationNet multiplier = 1.1 × 1.2 = 1.32 → 32% increase.
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Q8 Medium
A population of 10,000 first increases by 5% and then decreases by 5%. What is the final population?
ExplanationFinal = 10,000 × 1.05 × 0.95 = 10,000 × 0.9975 = 9,975. -
Q9 Hard
If a number is increased by 50% and then decreased by 50%, the net change is:
ExplanationNet multiplier = 1.5 × 0.5 = 0.75 → 25% decrease. -
Q10 Hard
The price is reduced by 20% and then increased by 25%. What is the net percentage change?
ExplanationNet multiplier = 0.8 × 1.25 = 1.0 → no net change. -
Q11 Hard
A value of Rs. 1,000 is increased by 10% and then decreased by 10%. What is the final value?
ExplanationFinal = 1,000 × 1.1 × 0.9 = Rs. 990. -
Q12 Hard
Three successive changes of +10%, +20%, and −5% give a net change of:
ExplanationNet multiplier = 1.1 × 1.2 × 0.95 = 1.254 → 25.4% increase. -
Q13 Hard
An article's price is first cut by 10% and then by another 20%. The net decrease is:
ExplanationNet multiplier = 0.9 × 0.8 = 0.72 → 28% decrease. -
Q14 Medium
Starting at 400, a number increases by 25% and then decreases by 20%. The final value is:
ExplanationFinal = 400 × 1.25 × 0.8 = 400.
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DS1 Easy
What is the net percentage change after two successive changes?
Statement IThe value is first increased by 20%.
Statement IIIt is then decreased by 20%.
ExplanationNet multiplier = 1.2 × 0.8 = 0.96 → 4% decrease. Both rates are needed. -
DS2 Medium
What is the final salary?
Statement IThe original salary is Rs. 20,000.
Statement IIIt receives successive increases of 10% and 20%.
ExplanationFinal = 20,000 × 1.1 × 1.2 = Rs. 26,400. Both original and rates are required.
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DS3 Easy
Is the net change zero?
Statement IA price is increased by 25% and then decreased by 20%.
Statement IIA price is decreased by 20% and then increased by 25%.
ExplanationBoth pairs give multiplier 1.0, so net change is zero in each case. Either statement alone is sufficient. -
DS4 Medium
What is the final population?
Statement IThe initial population is 10,000.
Statement IIIt changes by +5% and then −5%.
ExplanationFinal = 10,000 × 1.05 × 0.95 = 9,975. Both statements are needed.