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 EasyThe price of an article is first increased by 20% and then decreased by 20%. If the original price of the article is Rs. 500, what is the net percentage change in the price?ExplanationNet multiplier = 1.2 × 0.8 = 0.96. Same x% up then down always gives x²/100% decrease → 4% decrease. Rs. 500 becomes Rs. 480.
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Q2 EasyThe price of a shirt is increased by 20% and then decreased by 20%. What is the net percentage change in the price?ExplanationUsing successive change: 20 − 20 − (20×20)/100 = −4%. Final price is 96% of the original.
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Q3 EasyIf the price of a commodity increases by 10% and then decreases by 10%, what is the net change in price?ExplanationNet multiplier = 1.1 × 0.9 = 0.99 → 1% decrease. The second change is applied on the increased base.
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Q4 EasyA number is decreased by 10% and then increased by 10%. The net change is:ExplanationOrder does not matter for equal magnitudes: 0.9 × 1.1 = 0.99 → 1% decrease.
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Q5 MediumThe price of an article is first increased by 25% and then decreased by 20%. What is the net percentage change in the price?ExplanationNet multiplier = 1.25 × 0.8 = 1.0. The two changes cancel exactly.
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Q6 MediumSuccessive increases of 10% and 20% are equivalent to a single increase of:ExplanationNet = 10 + 20 + (10×20)/100 = 32%. Multiplier = 1.1 × 1.2 = 1.32.
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Q7 MediumA 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.
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Q8 MediumAn 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.
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Q9 MediumA 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.
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Q10 MediumStarting 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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Q11 HardA number is increased by 50% and then decreased by 50%. The net change is:ExplanationNet multiplier = 1.5 × 0.5 = 0.75 → 25% decrease. Same-percent rule: (50/10)² = 25% loss.
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Q12 HardA 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.
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Q13 HardThree 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.
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Q14 HardAn 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.
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DS1 Easy
The price of an article is changed twice in succession. What is the net percentage change in the price?
Statement IThe price is first increased by 20%.
Statement IIIt is then decreased by 20%.
ExplanationNet multiplier = 1.2 × 0.8 = 0.96 → 4% decrease. Each statement gives only one rate; both are needed. -
DS2 Easy
After two successive percentage changes, 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 sequences give multiplier 1.25 × 0.8 = 1.0 (or 0.8 × 1.25 = 1.0). Either statement alone confirms zero net change.
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DS3 Medium
An employee's monthly salary undergoes two successive percentage increases. What is the final salary?
Statement IThe original salary is Rs. 20,000.
Statement IIThe salary receives successive increases of 10% and 20%.
ExplanationFinal = 20,000 × 1.1 × 1.2 = Rs. 26,400. Statement I gives the base; Statement II gives the rates. Both are required. -
DS4 Medium
A town's population undergoes two successive percentage changes. What is the final population?
Statement IThe initial population is 10,000.
Statement IIThe population increases by 5% and then decreases by 5%.
ExplanationFinal = 10,000 × 1.05 × 0.95 = 9,975. Statement I gives the base; Statement II gives both rates. Together they determine the answer.