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30 Percentages Questions and Answers
30 solved Percentages questions with step-by-step explanations. Includes formulas, shortcuts, and tips for placement tests and competitive exams.
Advanced percentages questions for experienced learners. These medium-to-hard questions test deeper understanding and are ideal for those who have already mastered the basics. Each question includes a detailed explanation.
Key Formulas
Percentage = (Value / Total) × 100
New Value = Original × (100 ± P) / 100
For increase: multiply by (100 + P)/100. For decrease: multiply by (100 - P)/100
Discount = Marked Price - Selling Price
Successive change: Net% = a + b + (a × b)/100
Fraction equivalents: 50% = 1/2, 25% = 1/4, 20% = 1/5, 10% = 1/10
Q1
Medium
A quantity 160 is increased by 5%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 160 x (100+5)/100 = 168.
Q2
Medium
After a discount of 25%, the value changes from 380 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 380 x (100-25)/100 = 285.
Q3
Medium
A quantity 620 is increased by 30%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 620 x (100+30)/100 = 806.
Q4
Medium
What is 40% of 740?
Explanation:
A percentage means 'per hundred'. To find a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply. 40% of 740 = (40/100) x 740 = 296.
Q5
Medium
After a discount of 10%, the value changes from 500 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 500 x (100-10)/100 = 450.
Q6
Medium
A quantity 260 is increased by 10%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 260 x (100+10)/100 = 286.
Q7
Medium
After a discount of 10%, the value changes from 1160 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 1160 x (100-10)/100 = 1044.
Q8
Medium
A quantity 660 is increased by 10%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 660 x (100+10)/100 = 726.
Q9
Medium
After a discount of 10%, the value changes from 840 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 840 x (100-10)/100 = 756.
Q10
Medium
A quantity 480 is increased by 25%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 480 x (100+25)/100 = 600.
Q11
Medium
After a discount of 10%, the value changes from 560 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 560 x (100-10)/100 = 504.
Q12
Medium
A quantity 1040 is increased by 10%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 1040 x (100+10)/100 = 1144.
Q13
Medium
What is 40% of 920?
Explanation:
A percentage means 'per hundred'. To find a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply. 40% of 920 = (40/100) x 920 = 368.
Q14
Medium
A quantity 240 is increased by 30%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 240 x (100+30)/100 = 312.
Q15
Medium
After a discount of 10%, the value changes from 680 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 680 x (100-10)/100 = 612.
Q16
Medium
A quantity 360 is increased by 25%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 360 x (100+25)/100 = 450.
Q17
Medium
What is 40% of 720?
Explanation:
A percentage means 'per hundred'. To find a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply. 40% of 720 = (40/100) x 720 = 288.
Q18
Medium
After a discount of 5%, the value changes from 880 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 880 x (100-5)/100 = 836.
Q19
Medium
A quantity 560 is increased by 20%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 560 x (100+20)/100 = 672.
Q20
Medium
After a discount of 15%, the value changes from 680 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 680 x (100-15)/100 = 578.
Q21
Medium
A quantity 1100 is increased by 15%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 1100 x (100+15)/100 = 1265.
Q22
Medium
After a discount of 25%, the value changes from 1060 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 1060 x (100-25)/100 = 795.
Q23
Medium
A quantity 980 is increased by 30%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 980 x (100+30)/100 = 1274.
Q24
Medium
After a discount of 20%, the value changes from 540 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 540 x (100-20)/100 = 432.
Q25
Medium
A quantity 700 is increased by 20%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 700 x (100+20)/100 = 840.
Q26
Medium
What is 20% of 880?
Explanation:
A percentage means 'per hundred'. To find a percentage of a number, convert the percentage to a decimal by dividing by 100, then multiply. 20% of 880 = (20/100) x 880 = 176.
Q27
Medium
After a discount of 30%, the value changes from 680 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 680 x (100-30)/100 = 476.
Q28
Medium
A quantity 1040 is increased by 30%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 1040 x (100+30)/100 = 1352.
Q29
Medium
After a discount of 5%, the value changes from 260 to what?
Explanation:
To find the value after a discount, multiply the original value by (100 ± percentage) ÷ 100. Reduced value = 260 x (100-5)/100 = 247.
Q30
Medium
A quantity 500 is increased by 15%. What is the new value?
Explanation:
To find the value after a increase, multiply the original value by (100 ± percentage) ÷ 100. New value = 500 x (100+15)/100 = 575.
Key Takeaways
- Convert percentages to fractions for faster mental math: 25% = 1/4, 20% = 1/5, 10% = 1/10.
- For increase: multiply by (100 + p)/100. For decrease: multiply by (100 - p)/100.
- To find original after a change: divide the final value by (100 ± p)/100.
- Discount is always calculated on Marked Price, not Cost Price.
- Successive percentage change uses the formula: Net% = a + b + ab/100.
Frequently Asked Questions
What is the formula for percentage?
Percentage = (Value ÷ Total) × 100. For example, to find what percentage 30 is of 150: (30 ÷ 150) × 100 = 20%.
How do I calculate percentage increase?
Percentage increase = (New Value - Original Value) ÷ Original Value × 100. If a product increases from Rs. 200 to Rs. 250: Increase = 50, Percentage increase = (50 ÷ 200) × 100 = 25%.
How do I calculate percentage decrease?
Percentage decrease = (Original Value - New Value) ÷ Original Value × 100. For example, if a price drops from Rs. 500 to Rs. 400: Decrease = 100, Percentage decrease = (100 ÷ 500) × 100 = 20%.
What is the shortcut for 10%, 25%, and 50%?
10% = divide by 10. 25% = divide by 4 (one-fourth). 50% = divide by 2 (half). 20% = divide by 5. Use these fraction equivalents instead of always calculating (X ÷ 100) to save time.
How do I find the original amount after a percentage change?
If final value = Original × (100 ± p) ÷ 100, then Original = Final × 100 ÷ (100 ± p). For example, if Rs. 880 is the price after a 10% increase: Original = 880 × 100 ÷ 110 = Rs. 800.
What is successive percentage change?
When two percentage changes happen one after another, use: Net change = a + b + (a × b) ÷ 100. For increases of 10% followed by 20%: Net = 10 + 20 + (10 × 20) ÷ 100 = 32% increase. For decreases, use negative values.
More Percentages Practice Resources
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