Calculating percentage
To find what percentage A is of base B, keep B in the denominator.
(A / B) x 100
The word after 'of' or 'than' usually points to the base. What percent of 50 is 10? Base is 50.
Quantitative Aptitude
Master percentage fundamentals, base-change logic, fraction conversions, successive change, and exam-speed shortcuts.
Percentages measure a quantity as a fraction of 100 and are the single most reused concept in aptitude tests. They appear inside profit & loss, interest, data interpretation, elections, population growth, and mixture problems. The core skills are choosing the correct base, converting between percentages and fractions, applying multiplying factors for compound changes, and handling reverse-basis ("more than / less than") comparisons. Most percentage questions can be solved mentally once the base logic and the common fraction table are memorized.
Percent means per hundred. A percentage is a fraction whose denominator is 100, so the main skill is identifying the correct base.
To find what percentage A is of base B, keep B in the denominator.
The word after 'of' or 'than' usually points to the base. What percent of 50 is 10? Base is 50.
To measure increase or decrease, compare the change against the original value.
If price drops from 80 to 60, change is 20 and base is 80, so the decrease is 25%.
Instead of calculating a percentage and then adding or subtracting it, multiply by a factor. This makes compound changes much faster.
For an R% increase, multiply by the increase factor.
10% increase -> x 1.10, 25% increase -> x 1.25, 100% increase -> x 2.
For an R% decrease, multiply by the decrease factor.
10% decrease -> x 0.90, 25% decrease -> x 0.75, 5% decrease -> x 0.95.
Memorize the high-frequency conversions and rate patterns so calculations become instant during timed tests.
| 1/2 | 50% |
| 1/3 | 33.33% |
| 1/4 | 25% |
| 1/5 | 20% |
| 1/6 | 16.66% |
| 1/7 | 14.28% |
| 1/8 | 12.5% |
| 1/9 | 11.11% |
| 1/10 | 10% |
| 1/11 | 9.09% |
| 1/12 | 8.33% |
| 1/20 | 5% |
| 2/3 | 66.66% |
| 3/4 | 75% |
| 2/5 | 40% |
| 3/5 | 60% |
| 4/5 | 80% |
| 5/6 | 83.33% |
| 3/8 | 37.5% |
| 5/8 | 62.5% |
| 7/8 | 87.5% |
Use when a value must be expressed as a percentage of a base.
Use signed values for increase or decrease.
Use positive values for increase and negative values for decrease.
Convert 'A is R% more/less than B' into the reverse comparison.
The recurring question patterns in this topic — know the shape of each pattern before you solve.
Find x% of a given quantity by using 1%, 10%, or fraction conversions.
What is 30% of 250? → 10% is 25 ×3 → 75.
Find the percentage by which a value changed, always comparing with the original value.
200 → 250 is a change of 50 on base 200, i.e. 25%.
Two or more percentage changes applied one after another; net change differs from the simple sum.
+10% then −10% nets to −1%.
Convert "A is R% more than B" into "B is R/(100+R)% less than A".
If A is 25% more than B, B is 25/125 ×100 = 20% less than A.
Apply percentages to vote shares, year-on-year growth, and water/milk mixtures with a constant component.
Mixture with 10% water: add water until it becomes 20%.
High-signal questions with full solution flow across difficulty patterns.
Classic exam problems worth internalizing — each one ships a complete step-by-step solution.
Swap numbers when one side is easier to compute mentally.
A value increased by x% and then decreased by x% always goes down.
If price rises by R% and expenditure must stay same, reduce consumption by this amount.
Use when a deal says buy N and get M free.
Where most students lose marks — review these before you sit the test.
You have mastered the theory. Now put it under pressure with a focused topic test and instant explanations.
Take Percentages Test