Percentage change

NMAT Practice — Change in Percentage (20 Questions)

Click Show Solution to reveal the answer and the step-by-step explanation (solutions appear in green).

Important 

 Percentage Change = (New − Old) ÷ Old × 100%

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1. If the price of a shirt rises from ₹400 to ₹500, what is the percentage increase?

Increase = 500 − 400 = 100.
Percentage increase = (100 ÷ 400) × 100 = 25%.
Answer: 25%

2. A population increases from 20,000 to 22,600. What is the percent increase?

Increase = 22,600 − 20,000 = 2,600.
Percent = (2,600 ÷ 20,000) × 100 = 13%.
Answer: 13%

3. An item's price is decreased from ₹1500 to ₹1200. What is the percentage decrease?

Decrease = 1500 − 1200 = 300.
Percent decrease = (300 ÷ 1500) × 100 = 20%.
Answer: 20%

4. A phone's price is increased by 12%. If the original price was ₹25,000, what is the new price?

Increase = 12% of 25,000 = 0.12 × 25,000 = 3,000.
New price = 25,000 + 3,000 = ₹28,000.
Answer: ₹28,000

5. A salary was reduced by 8% resulting in ₹46,000. What was the original salary?

Let original = x. After 8% reduction: x × (1 − 0.08) = 46,000 → x × 0.92 = 46,000.
x = 46,000 ÷ 0.92 = ₹50,000.
Answer: ₹50,000

6. If a value decreases by 20% and then increases by 20%, is it back to the original value? If not, by what percent does it differ?

After −20%: factor = 0.80. Then +20%: multiply by 1.20 → overall factor = 0.80 × 1.20 = 0.96.
0.96 of original = 4% less than original.
Answer: No. It is 4% less than the original (net −4%).

7. A commodity's price is increased by 15% and then decreased by 15%. What is the net percentage change?

Factor = 1.15 × 0.85 = 0.9775 → overall = 97.75% of original.
Net change = 100% − 97.75% = 2.25% decrease.
Answer: 2.25% decrease (net −2.25%).

8. A discount of 25% is given on an item priced ₹800. What is the discounted price?

Discount = 25% of 800 = 0.25 × 800 = 200.
Sale price = 800 − 200 = ₹600.
Answer: ₹600

9. A population decreases by 10% each year. After 2 years, what is the remaining percentage of the original population?

Remaining factor after 1 year = 0.90. After 2 years = 0.90² = 0.81 → 81% of original.
Answer: 81% of the original

10. If an investment grows by 5% compound annually for 3 years, what is the total percentage increase (approx)?

Factor = (1 + 0.05)³ = 1.157625 → increase = 0.157625 = 15.7625% ≈ 15.76%.
Answer: ≈ 15.76% increase

11. A price is first increased by 20% and then by 10%. What is the overall percent increase?

Factor = 1.20 × 1.10 = 1.32 → net increase = 32%.
Answer: 32%

12. A trader marks up cost price by 40% and offers a 10% discount on the marked price. What is the net profit percentage?

Cost → Marked price factor = 1.40. After 10% discount: selling factor = 1.40 × 0.90 = 1.26.
Profit = 1.26 − 1 = 0.26 = 26%.
Answer: 26% profit

13. If a number is increased by 50% and then decreased by 40%, what's the net change percentage?

Factor = 1.50 × 0.60 = 0.90 → net = 0.90 − 1 = −0.10 = −10% (10% decrease).
Answer: 10% decrease (net −10%)

14. A value decreases from 500 to 350. What is the percentage decrease?

Decrease = 500 − 350 = 150.
Percent = (150 ÷ 500) × 100 = 30%.
Answer: 30%

15. To increase 240 to 300, by what percent should it be increased?

Increase = 300 − 240 = 60.
Percent = (60 ÷ 240) × 100 = 25%.
Answer: 25%

16. If a population decreases by 15% and then increases by 15%, what's the net effect?

Factor = 0.85 × 1.15 = 0.9775 → net is 97.75% of original → 2.25% decrease.
Answer: 2.25% decrease (net −2.25%).

17. A laptop priced at ₹60,000 is given a 12.5% discount. What's the sale price?

Discount = 12.5% of 60,000 = 0.125 × 60,000 = 7,500.
Sale price = 60,000 − 7,500 = ₹52,500.
Answer: ₹52,500

18. A commodity's price rises by 30% then falls by 20%. What is the net percentage change?

Factor = 1.30 × 0.80 = 1.04 → net = 1.04 − 1 = 0.04 = 4% increase.
Answer: 4% increase

19. If a salary increases from ₹35,000 to ₹42,000, find the percentage increase.

Increase = 42,000 − 35,000 = 7,000.
Percent = (7,000 ÷ 35,000) × 100 = 20%.
Answer: 20%

20. A shirt's price is decreased by 10% and then decreased again by 10%. What's the total percent decrease?

Remaining factor = 0.9 × 0.9 = 0.81 → remaining = 81% → total decrease = 19%.
Answer: 19% decrease

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