Percentage literally means "per hundred" — per centum in Latin. When you say 40%, you mean 40 out of every 100 parts. That is the entire idea. Everything else is just applying this ratio in different contexts.
Here is an analogy that sticks: imagine a glass that holds 100 ml. If 25 ml of water is in it, it is 25% full. If the glass holds 200 ml but still has 25 ml, the glass is only 12.5% full. The percentage depends on what the whole (the base) is — same absolute number, different percentage, different base. This is the single most important intuition for this chapter.
Percentage is not a unit. It is a ratio scaled to 100. So 25% = 25/100 = 1/4 = 0.25. These four forms — percentage, fraction, decimal, and ratio — are interchangeable. You need to move between them fluently in the exam.
Why does SSC CHSL care about this? Because percentage is the engine running behind Profit & Loss, Simple Interest, Data Interpretation, and Discount questions. If you are slow on basic percentage arithmetic, those chapters will also be slow. Get this chapter to a point where simple percent calculations feel automatic — not thought about, just done.
The three core operations you will be tested on:
x% of N?A of B?All eight PYQs in this topic fall into these three buckets. Master these, and percentage will never cost you marks.
Formula 1 — Finding x% of N:
This is straightforward. The trap is losing track of the base. "25% of 80" has a base of 80. Do not divide 25 by 80 — that gives you something else entirely.
Formula 2 — Expressing A as a percent of B:
Always ask yourself: "percent of what?" The "of what" is your denominator. In "what percentage of 1 hour is 15 minutes?", 1 hour (= 60 minutes) is the base, so: (15/60) × 100 = 25%.
Formula 3 — Percentage change:
If the result is positive, it is an increase. If negative, it is a decrease. The denominator is always the original (old) value — never the new one. This is where most mistakes happen.
You need to memorize these cold. Recognizing 12.5% = 1/8 or 33.33% = 1/3 instantly saves 20-30 seconds per question.
| Fraction | Decimal | Percentage |
|----------|---------|------------|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333... | 33.33% |
| 1/4 | 0.25 | 25% |
| 1/5 | 0.2 | 20% |
| 1/6 | 0.1666... | 16.67% |
| 1/7 | 0.1428... | 14.28% |
| 1/8 | 0.125 | 12.5% |
| 1/9 | 0.111... | 11.11% |
| 1/10 | 0.1 | 10% |
| 3/4 | 0.75 | 75% |
| 2/3 | 0.666... | 66.67% |
When you see 12.5% of 800, do not reach for the division. Recognize 12.5% = 1/8, then 800 ÷ 8 = 100. Done in one step.
This is the "reverse percentage" type. "30% of a number is 90, find 50% of that number."
Step 1: Find the whole number. If 30% = 90, then 1% = 90/30 = 3, so 100% = 300.
Step 2: Find the required percent. 50% of 300 = 150.
The key move: get to either 1% or 100% first, then scale.
"A value increases by x%" means the new value is (100 + x)% of the original.
New value = Original × (100 + x)/100
So an 80 cm length increased by 25%:
80 × (125/100) = 80 × 1.25 = 100 cm
You can also compute it as 80 + 25% of 80 = 80 + 20 = 100. Both approaches work; the multiplier method (100 ± x)% is faster for chained percentage problems in DI questions.
0.35 × 100 = 35%.(3/4) × 100 = 75%.35% ÷ 100 = 0.35.75% = 75/100 = 3/4.These conversions appear directly as one-liner questions in SSC CHSL and also embedded inside longer problems.
Here is a powerful symmetry most students never use: x% of y = y% of x. So 4% of 75 = 75% of 4 = 3.
When to use it: one of the two numbers is a "nice" percentage (25, 50, 75) and the other is awkward. Flip to make the multiplication easier.
Micro-example: 4% of 25 looks annoying. Flip to 25% of 4 = 1. Done instantly.
Standard method: 4/100 × 25 = 100/100 = 1 — requires fraction arithmetic. Shortcut: mental flip, answer in under 3 seconds vs. 15 seconds standard.
Memorize the table: 12.5% = 1/8, 25% = 1/4, 33.33% = 1/3, 16.67% = 1/6, 75% = 3/4.
When to use it: any "find x% of N" problem where x is a common benchmark percentage.
Micro-example: 12.5% of 800. Recognize 12.5% = 1/8. Then 800 ÷ 8 = 100. No multiplication at all.
Standard method: (12.5/100) × 800 involves decimal multiplication — 4-5 steps, ~25 seconds. Fraction shortcut: 1 step, ~5 seconds.
When to use it: "x% of N" where x is not a benchmark fraction, OR when you need to find the original number from a given percentage.
Method: Find 1% of the number first (divide by 100), then scale.
Micro-example: 7% of 350. First, 1% of 350 = 3.5. Then 7 × 3.5 = 24.5.
For reverse: "30% of a number is 90." 1% = 90/30 = 3, so 100% = 300. This anchors all further calculations without setting up a full equation.
Standard method: cross-multiply algebraically — 3-4 lines. The 1% anchor: 2 mental steps.
The single most common trap in percentage change questions: students divide by the new value instead of the original.
When to use it: any question asking "by what percent did it increase/decrease?"
Worked example: Price goes from ₹200 to ₹250. Change = ₹50. Percentage change = 50/200 × 100 = 25%, NOT 50/250 × 100 = 20%.
Rule: the denominator is always the starting point — the value you are measuring the change FROM. If it says "what percent did it increase?", the base is the smaller (original) number.
Step count difference: getting this rule right eliminates re-doing the problem — saves 30-45 seconds when you catch the trap before calculating.
When to use it: questions that give you an original value and ask for the new value after a % change.
Convert the percentage change into a multiplier: increase by x% → multiply by (100+x)/100; decrease by x% → multiply by (100-x)/100.
Micro-example: original length 80 cm, increase by 25%. Multiplier = 125/100 = 5/4. New value = 80 × 5/4 = 100 cm. One multiplication, no addition step needed.
Standard method: find 25% of 80 = 20, then add 80 + 20 = 100. That is two operations. Multiplier method: one multiplication — saves a step, reduces arithmetic error.
Read the question and immediately classify it into one of these three types:
Type 1 — "Find x% of N": Check if x matches a fraction in your table (25, 50, 75, 12.5, 33.33, 16.67, 20). If yes, convert and divide. If no, use the 1% anchor and scale.
Type 2 — "A is what % of B?": Write (A/B) × 100. Make sure you identify the base (B) correctly — it is the "of what" in the question. Units must match before dividing.
Type 3 — "% change from old to new": Compute (New - Old)/Old × 100. Never divide by the new value. If the question says "increased by x%, find the new value", use the multiplier (100+x)/100 × old.
Type 4 — "Reverse: x% of a number is given, find y% of it": Get to 1% first, then scale to 100% to find the number, then compute y%.
Decision: if the answer options are very spread out (differ by more than 10), you can estimate to eliminate two options and then verify one. If options are close, compute exactly.
Why this question: The most direct "find x% of N" question — tests the basic formula and option 1 of the fraction table.
Solving path: Recognize 25% = 1/4. So 1/4 of 80 = 20. Do not divide 25 by 80. Answer: option B (20).
Why this question: Tests whether you correctly identify the base. Many students write (60/15) × 100 instead of (15/60) × 100 — classic inversion trap.
Solving path: "What percentage of 1 hour" — the base is 1 hour = 60 minutes. Formula: (15/60) × 100 = 25%. Answer: option B (25%).
Why this question: Tests fraction recognition. 12.5% is 1/8 — if you see this immediately, the problem is a single division.
Solving path: 12.5% = 1/8. Then 800 ÷ 8 = 100. Answer: option B (100).
Why this question: Direct fraction-to-percentage conversion. Appears regularly as a one-liner in CHSL.
Solving path: (3/4) × 100 = 75%. Answer: option D (75%). If you have the table memorized, this is a 2-second question.
Why this question: Decimal-to-percent conversion and percentage change combined in the same paper — know both directions.
Solving path: 0.35 × 100 = 35%. Answer: option B (35%).
Why this question: Percentage increase applied to a measurement. Tests the multiplier method and whether you add correctly.
Solving path: New length = 80 × (125/100) = 80 × 5/4 = 100 cm. Alternatively: 25% of 80 = 20, so new = 80 + 20 = 100 cm. Answer: option C (100 cm).
Why this question: Tests the percentage change formula and the base-identification trap directly.
Solving path: Increase = ₹250 - ₹200 = ₹50. Base = original price = ₹200. Percentage increase = (50/200) × 100 = 25%. Answer: option B (25%). Dividing by 250 gives 20% — wrong.
Why this question: Two-step reverse percentage. First find the whole number, then compute a different percentage of it.
Solving path: 30% of N = 90, so N = 90 × 100/30 = 300. Then 50% of 300 = 150. Answer: option D (150). The 1% anchor: 1% = 3, 50% = 150.
Dividing by the new value in percentage change problems. The formula is always (change/original) × 100. If a price goes from ₹200 to ₹250, the base is ₹200, not ₹250. Dividing by 250 gives you a wrong answer that will appear as a distractor option.
Unit mismatch before dividing. In "what percentage of 1 hour is 15 minutes?", you cannot write 15/1 — you must convert 1 hour to 60 minutes first. Always unify units before applying the formula.
Confusing "A is x% more than B" with "A is x% of B". "A is 25% more than B" means A = 1.25B. "A is 25% of B" means A = 0.25B. These differ by a factor of 5 — the error completely destroys the answer.
Wrong direction in "x% of what = given value" problems. If 30% of N = 90, then N = 90 × 100/30 = 300. Students often compute 90 × 30/100 = 27 instead — multiplying in the wrong direction.
Not simplifying units in "what percent is A of B" problems when both are in different sub-units. For example, comparing 500 grams to 2 kg: convert to the same unit first (500 g and 2000 g), then take the ratio.
Picking the fraction reciprocal. When recognizing 12.5% = 1/8, the operation is ÷ 8, not × 8. With 25% = 1/4, you divide by 4. Confirm direction: percentage less than 100% always gives an answer smaller than the original number.