Percentages
Percentages are the single most reused idea in the entire CAT Quant section. A "percent" simply means "out of 100", so every percentage is just a fraction with a denominator of 100 — and once you see it that way, profit-loss, interest, mixtures, data interpretation and even ratio questions all become the same skill in different clothes. CAT rarely asks a plain "find 20% of 80"; instead it hides percentages inside multi-step word problems and rewards students who can convert between fractions, decimals and percentages instantly, handle successive changes without errors, and work backwards from a final value. This chapter builds that fluency from the ground up: the conversions, the change formulas, the successive-change shortcut, reverse percentages, and the high-frequency CAT applications — each with worked examples, the fastest mental method, and the traps that cost careless students marks.
Topics
⚡ CAT shortcuts & speed methods
The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.
- Memorise the 1/n table to 1/12 — read every percentage as a fraction (37.5% = 3/8, 16⅔% = 1/6).
- Successive change a%, b% → a + b + ab/100. Two equal +x% changes → 2x + x²/100.
- Reverse percentage: always DIVIDE by (1 ± x/100). Never add the percentage back to the final value.
- Product constant: price ↑ p% ⇒ consumption ↓ p/(100+p); price ↓ p% ⇒ consumption ↑ p/(100−p).
- "A is x% more than B" ⇒ "B is x/(100+x) less than A". Learn the pairs: +25%↔−20%, +33⅓%↔−25%, +50%↔−33⅓%.
- For word problems, set the unknown whole = 100 (or the LCM of denominators) so percentages become clean integers.
⚠️ Common mistakes & traps
CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.
- Adding successive percentages (20% + 30% ≠ 50%; it is 56%).
- Thinking +x% then −x% returns to the start — it always ends lower by x²/100 %.
- In reverse percentage, adding x% to the final value instead of dividing by (1 ± x/100).
- Confusing "x% more than B" with "B is x% less than A" — the base changes.
- Forgetting to convert to a common unit before forming the ratio (kg vs g, hours vs minutes).
📈 CAT exam insight & PYQ analysis
🎴 Flashcards — instant recall
Tap a card to reveal the answer. Drill these until they are automatic.
📌 Quick revision
Chapter test
🏆 Vidaara CAT success checklist
You have truly mastered Percentages when you can tick every box below.
- Recall every formula in this chapter without looking them up
- Solve each topic’s practice set with at least 80% accuracy
- Use the chapter shortcuts to cut your solving time in half
- Spot and avoid every common trap listed above
- Score 80%+ on the timed chapter test
📋 Chapter mastery scorecard
Track where you stand. Aim for the target before moving to the next chapter.
| Skill checkpoint | Target |
|---|---|
| Concept theory & formulas understood | 100% |
| Topic practice sets attempted (5 topics) | 5/5 |
| Best topic-test score | — → 80%+ |
| Chapter test score | — → 80%+ |
| Flashcards drilled to instant recall | 12 cards |
Formula Reference Sheet
Core conversions & change
| Percentage of a number | x% of N = (x/100) × N |
|---|---|
| Value as a percentage | (Part / Whole) × 100 % |
| Percentage change | (New − Old) / Old × 100 % |
| Increase by x% | N × (1 + x/100) |
| Decrease by x% | N × (1 − x/100) |
CAT power-tools
| Successive change a% then b% | net = a + b + ab/100 (%) |
|---|---|
| Reverse percentage | Original = Final / (1 ± x/100) |
| A is x% more than B | B is [x/(100+x)]×100 % less than A |
| A is x% less than B | B is [x/(100−x)]×100 % more than A |
| Product constant (price↑ p% ⇒ consumption↓) | [p/(100+p)]×100 % |