Percentage Shortcuts That Actually Save Time in Aptitude Tests
Percentages are the highest-leverage topic in quantitative aptitude, for a boring reason: profit and loss, simple and compound interest, discounts, and most data interpretation are all percentages wearing a different hat. Get fast here and four other topics get faster.
“Fast” is the operative word. In a test you might have 60–70 seconds per question. That’s not enough time to write out (x/100) × y and do long multiplication. It is enough time if you’ve internalised three things.
1. The fraction table (memorise this one)
Most percentage arithmetic in aptitude tests is designed around clean fractions. 37.5% of 64 looks like a calculator question. As 3/8 × 64 = 24, it’s a two-second question.
| Fraction | Percent | Fraction | Percent |
|---|---|---|---|
| 1/2 | 50% | 1/9 | 11.11% |
| 1/3 | 33.33% | 1/10 | 10% |
| 1/4 | 25% | 1/11 | 9.09% |
| 1/5 | 20% | 1/12 | 8.33% |
| 1/6 | 16.67% | 1/16 | 6.25% |
| 1/7 | 14.28% | 3/8 | 37.5% |
| 1/8 | 12.5% | 5/8 | 62.5% |
Worked examples:
- 16.67% of 48 →
1/6 × 48= 8 - 62.5% of 88 →
5/8 × 88= 55 - 12.5% of 96 →
1/8 × 96= 12
The moment you see 33.33, 16.67, 12.5, 37.5 or 62.5 in a question, stop and convert. The number was chosen to be clean; the test-setter is telling you which method they expect.
2. Successive changes: a + b + ab/100
Two percentage changes applied one after another do not add up. This is the single most common trap in the topic.
A price increases by 20%, then decreases by 20%. What’s the net change?
The instinct says zero. The answer is:
net = a + b + (a × b)/100
= 20 + (−20) + (20 × −20)/100
= −4%
A 4% decrease. The second 20% is taken off a bigger number than the first was added to, so you don’t get back where you started. Sanity check: 1.2 × 0.8 = 0.96.
More examples:
- +10% then +20% →
10 + 20 + 200/100= +32% (check:1.1 × 1.2 = 1.32) - +10% then −10% →
10 − 10 − 100/100= −1% - +20% then −25% →
20 − 25 − 500/100= −10% (check:1.2 × 0.75 = 0.9)
Signs matter: a decrease goes in as a negative number, and the ab/100 term inherits that sign. For three successive changes, apply the formula to the first two, then apply it again with the result.
3. Product constancy: the “more than / less than” reversal
This is the family of questions that eats time because people set up equations for it.
A is 25% more than B. By what percent is B less than A?
Not 25%. The two percentages have different bases — the first is a percentage of B, the second is a percentage of A. The formula:
If A is x% MORE than B, then B is x/(100 + x) × 100 % less than A.
If A is x% LESS than B, then B is x/(100 − x) × 100 % more than A.
So A is 25% more than B → B is 25/125 × 100 = 20% less than A.
And the mirror: A’s salary is 20% less than B’s → B’s is 20/80 × 100 = 25% more than A’s.
The fraction table makes this instant. 25% is 1/4, so “25% more” means the ratio is 4:5, so going the other way is 1/5 = 20% less. You can do the whole thing in your head by thinking in ratios instead of percentages.
The same idea powers the classic expenditure question:
The price of sugar rises by 25%. By how much must a family cut consumption to keep expenditure unchanged?
Expenditure = price × consumption. For the product to stay constant when price becomes 5/4 of itself, consumption must become 4/5 of itself — a 20% cut. Same numbers as before, and no equation.
The trap underneath all three
Every mistake in this topic is a base mistake — using the wrong number as the 100%.
“Increased from 40 to 50” is a 25% increase (10 out of 40). “Decreased from 50 to 40” is a 20% decrease (10 out of 50). Same two numbers, same gap of 10, different answers — because the base changed.
Before you compute anything, say out loud: percent of what? That one habit prevents most of the errors people blame on carelessness.
Now do them under time pressure
Reading this changes nothing on its own — this is a speed skill, and speed only comes from reps.
Try the percentages quiz — it’s timed, it explains every answer on the spot, and it’ll tell you fairly quickly whether the fraction table is actually in your head or just on this page. Then take the same skill into a real company pattern with the TCS or Infosys practice sets, where percentages turn up inside longer word problems.