Percentage questions with answers and concepts

Learn percentage with concept notes and worked examples, then practise focused questions with explained answers. Build accuracy for placement and competitive aptitude tests before trying timed mode.

174 practice questionsPage updated 11 Nov 2026Review metadata pendingPractice questions

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Percentage is one of the most important topics in quantitative aptitude, forming the foundation for many other concepts like profit and loss, simple and compound interest, and data interpretation. A percentage represents a fraction with 100 as its denominator, making it a standardised way to compare quantities and express proportions.

Key formulas and rules

11 rules

Percentage $= \frac{Part}{Whole} \times 100$

Part $= \frac{Percentage}{100} \times Whole$

Percentage Increase $= \frac{New Value - Original Value}{Original Value} \times 100$

Percentage Decrease $= \frac{Original Value - New Value}{Original Value} \times 100$

If a value increases by $x %$ and then decreases by $x %$ , net effect $= - \frac{x ^{2}}{100} %$ (always a net loss)

Successive percentage change: $a %$ followed by $b %$ gives $(a + b + \frac{ab}{100}) %$

If A is $x %$ more than B, then B is $\frac{x}{100 + x} \times 100%$ less than A

If A is $x %$ less than B, then B is $\frac{x}{100 - x} \times 100%$ more than A

Successive discounts of $d_{1} %$ and $d_{2} %$ give single equivalent discount: $(d_{1} + d_{2} - \frac{d _{1} d _{2}}{100}) %$

To reverse a percentage increase of $x %$ : multiply by $\frac{100}{100 + x}$

To reverse a percentage decrease of $x %$ : multiply by $\frac{100}{100 - x}$

Key concepts

Basic Percentage Calculations

Converting fractions to percentages: multiply by 100. Converting percentages to fractions: divide by 100. Common conversions to remember: 1/2 = 50%, 1/3 ~= 33.33%, 1/4 = 25%, 1/5 = 20%, 1/6 ~= 16.67%, $1/8 = 12$ .5%, 1/10 = 10%, 1/12 ~= 8.33%, $1/16 = 6$ .25%, 1/20 = 5%. These quick conversions save time during calculations.

Percentage Change

Percentage increase or decrease is always calculated with respect to the original value. The formula is: (Change/Original) x 100. A common mistake is using the new value as the base. Remember: increase of 50% followed by decrease of 50% does NOT bring you back to the original value - it results in a net loss of 25%.

Successive Percentages

When percentages are applied one after another (successive), they compound rather than simply add. For example, a 20% increase followed by a 30% increase is NOT 50%, but rather: 20 + 30 + (20x30)/100 = 56%. The formula for successive changes of a% and b% is: a + b + (ab/100). This applies to both increases and decreases (use negative for decreases).

Reverse Percentage (Finding Original Value)

When given a value after percentage change and asked to find the original: If final value is after x% increase, original = Final x 100/(100+x). If final value is after x% decrease, original = Final x 100/(100-x). This is crucial for problems stating 'after a 20% discount, the price is 400, find original price'.

Comparing Percentages

When A is x% more than B, B is NOT x% less than A. Use the formula: If A is x% more than B, then B is [x/(100+x)] x 100% less than A. Example: If A is 25% more than B, B is (25/125) x 100 = 20% less than A. This asymmetry is commonly tested in exams.

Percentage to Ratio and Vice Versa

Percentage expresses a proportion of a whole ( $25% = \frac{25}{100} = \frac{1}{4}$ of the total, representing a 1:4 part-to-whole relationship or a 1:3 part-to-part ratio). When converting a part-to-whole ratio like 3:5, express it as $\frac{3}{5} \times 100 = 60%$ . Always confirm whether a given ratio compares part to total or part to part.

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Worked examples

Example 1

A number is first increased by 20% and then decreased by 20%. What is the net percentage change in the number?

Solution

Step 1: Apply the successive percentage change formula.

Net Change = (a + b + \frac{ab}{100}) %

Step 2: Substitute $a = + 20$ and $b = - 20$ .

Net Change = (20 - 20 + \frac{20 \times ( - 20 )}{100}) % = (0 - \frac{400}{100}) % = - 4%

Alternative check with base 100:
- Initial value = $100$
- After $20%$ increase: $100 + 20 = 120$
- After $20%$ decrease: $120 - (0.20 \times 120) = 120 - 24 = 96$
- Net change: $96 - 100 = - 4%$

Answer: A 4% decrease.

Example 2

If the price of sugar increases by 25%, by what percentage must a household reduce its consumption to keep the total expenditure unchanged?

Solution

Step 1: Apply the expenditure invariance formula.

Required Reduction = (\frac{x}{100 + x}) \times 100%

Step 2: Substitute $x = 25$ .

Reduction = (\frac{25}{100 + 25}) \times 100% = \frac{25}{125} \times 100% = \frac{1}{5} \times 100% = 20%

Answer: 20%.

Example 3

A student's score in Mathematics increased from 60 to 75. What is the percentage increase in marks?

Solution

Step 1: Calculate the absolute increase.

Δ M = 75 - 60 = 15 marks

Step 2: Compute percentage increase over the baseline (60).

%Δ = \frac{Increase}{Original Value} \times 100% = \frac{15}{60} \times 100% = \frac{1}{4} \times 100% = 25%

Answer: 25% increase.

Example 4

After a discount of 15%, an article is sold for 340. What was its original marked price?

Solution

Step 1: Set up the equation with original price $x$ .

Selling Price = (100% - 15%) \times x = 0.85 x

Step 2: Solve for $x$ .

0.85 x = 340 ⟹ x = \frac{340}{0.85} = \frac{340 \times 100}{85} = 4 \times 100 = 400

Answer: 400.

Representative solved questions

See the kind of question in this topic before opening the full practice set.

Question 1

A price is first increased by 10% and then by 20%. What is the total percentage increase?

Answer: B. 32%

Explanation

Let original = 100
After 10% increase = 110
After 20% increase = 110 x 1.2 = 132
Total increase = 132 - 100 = 32%

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 2

If A is 20% more than B, then B is what percent less than A?

16.67%
20%
25%
30%

Answer: A. 16.67%

Explanation

Let $B = 100$
$A = 120$ (20% more than “20%”)
Difference = 120 - 100 = 20
B is less than “16.67%” by (20/120) x $100 = 16$ .67%

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Question 3

In an election, candidate A got 75% of the valid votes. If 15% of votes were invalid and A got 6375 valid votes, what was the total number of votes?

8000
9000
10000
12000

Answer: C. 10000

Explanation

Let total votes = x
Valid votes = 85% of $x = 0$ .85x
A got 75% of valid = 0.75 x 0.85x = 0.6375x
$0.6375 x = 6375$
$x = 10000$

Sources and review notes

This is an AISEA-authored practice question.

Review status: accepted · Reviewed 2026-08-13 · structure and answer-key checks, editorial quality checks, duplicate screening

Common mistakes and useful habits

Always identify the base (original) value before calculating percentage change - this is the most common source of errors
Memorise common fraction-percentage conversions (1/2 to 1/20) to speed up calculations significantly
For successive percentage changes, remember they compound - never simply add or subtract percentages directly
When a value changes by x% and then by y%, the net effect is always x + y + (xy/100) - use this to verify your answers
For 'maintaining expenditure' problems, use the formula: percentage decrease in consumption = [100x/(100+x)]% where x is the price increase percentage
Always check if your answer makes logical sense - a number cannot decrease by more than 100% (it would become negative)
When comparing two values where one is x% more than the other, the reverse relationship is never the same percentage - use x/(100+/-x) formula

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