Percentage is one of those topics where you already know the mechanics — what trips SSC CGL candidates is not the formula, it is recognizing which version of the formula applies in which disguise.
The word "percent" means "per hundred." When you say 40%, you mean 40 parts out of every 100. That is it. Every percentage problem is just a fraction with 100 in the denominator, written in a more readable way.
Here is the analogy that locks it in: think of 100 as your reference village of exactly 100 people. Any percentage question is asking you how many of those 100 people satisfy some condition. If 25% have phones, 25 people out of 100 have phones. If you add 20 more people to the village, you have to re-calculate the fraction against the new total — that is where percentage change questions come from.
The three core operations you need:
1. Converting between forms
3/4 × 100 = 75%75% = 75/100 = 3/40.75 → 75%2. Finding a percentage of a number
P% of X = (P/100) × X
This is the bedrock. Everything else builds on it.
3. Finding what percentage one number is of another
(Part / Whole) × 100 = Percentage
In CGL, these three operations get combined, chained, or disguised inside word problems about salaries, populations, prices, and mixtures. Your job is to strip away the story and identify which operation is being chained.
One important mindset shift: always ask "percentage of what?" before writing anything. The base (denominator) changes the entire answer. 20% of 500 and 20% of 600 give completely different numbers. In successive percentage change problems, the base keeps shifting — that is the trap.
This is the most tested single formula in SSC CGL percentage problems:
Percentage Change = [(New Value - Original Value) / Original Value] × 100
Positive result = increase. Negative result = decrease. Never put the new value in the denominator — it is always the original.
When a value is changed by a% first and then by b%, the net effect is NOT (a + b)%. The correct net percentage change is:
Net Change = a + b + (ab/100)%
Where a and b carry their signs (positive for increase, negative for decrease).
Example: 20% increase followed by 15% decrease.
Net = 20 + (-15) + [20 × (-15)/100] = 20 - 15 - 3 = 2% increase.
Standard method using 100 as base: 100 → 120 → 102. Net = 2% increase. Same answer, but the formula is faster once you internalize the sign rule.
Look — this is a dedicated exam trap. When price increases by r% and you want expenditure to stay constant, the reduction in consumption required is:
Reduction = [r / (100 + r)] × 100%
When price decreases by r% and you want expenditure to stay constant, the increase in consumption required is:
Increase = [r / (100 - r)] × 100%
Do not derive this in the exam. Memorize the template.
Example: Price rises 25%. Consumption reduction = 25/125 × 100 = 20%.
The standard mixture question gives you a solution of X% concentration and asks how much pure substance to add to reach Y% concentration.
Setup: Let the mixture volume be V and concentration be c₁%. You add x ml of pure substance (100% concentration) to reach c₂%.
(c₁/100 × V + x) / (V + x) = c₂/100
Solve for x. Always set up this equation from first principles — do not try to memorize a sub-formula, because the question can vary (adding water instead of pure substance, etc.).
"A is 25% more than B" means A = B × (1 + 25/100) = 1.25B.
"A is 25% less than B" means A = B × (1 - 25/100) = 0.75B.
Here is where candidates make the classic reversal error: "If A is 25% more than B, by what percentage is B less than A?"
B is less than A by: (A - B)/A × 100 = (0.25B/1.25B) × 100 = 20%
Not 25%. The base has shifted from B to A.
For a quantity growing at r% per year, after n years:
Final = Initial × (1 + r/100)ⁿ
For two years with the same rate, expand the square rather than computing step-by-step:
Final = Initial × (1 + r/100)²
For small r, the expansion gives: Initial × [1 + 2r/100 + r²/10000]
In the exam, two-year growth is almost always faster to compute step-by-step: Year 1 result × multiplier again. Three or more years, use the compound formula.
Selling Price = Marked Price × (1 - Discount%/100)
Profit% = (Selling Price - Cost Price)/Cost Price × 100
When a question gives you markup and discount together, chain the multipliers:
SP = CP × (1 + Markup%/100) × (1 - Discount%/100)
Plug CP = 100, compute SP, and the difference is the profit or loss percent directly.
Memorize these cold: 1/8 = 12.5%, 1/6 = 16.67%, 1/5 = 20%, 1/4 = 25%, 1/3 = 33.33%, 3/8 = 37.5%, 1/2 = 50%, 5/8 = 62.5%, 2/3 = 66.67%, 3/4 = 75%, 5/6 = 83.33%, 7/8 = 87.5%.
When a question says "40% of 250 = 20% of x", convert: 40% = 2/5, so (2/5 × 250) = (1/5 × x). Reading fractions instead of decimals takes 3 steps vs 5 steps in the standard approach. Standard method: 45s. This: 15s.
For two successive changes a% and b% (with signs): Net = a + b + ab/100.
Micro-example: 20% increase then 15% decrease. 20 + (-15) + (20×(-15)/100) = 5 - 3 = 2% increase. You skip the intermediate calculation entirely. Standard method (build 100 → 120 → 102): 4 steps. Formula: 1 step. Speed gain: standard 30s vs shortcut 8s.
If price rises by r%, consumption drop needed = r/(100+r) × 100. If price falls by r%, consumption rise needed = r/(100−r) × 100.
Micro-example: Price rises 25% → drop = 25/125 × 100 = 20%. If you set this up from scratch with variables, it costs 6 algebraic steps. The template collapses it to one division. Standard: 40s. Template: 8s.
Set CP = 100 always. Then SP = 100 × (1 + m/100) × (1 − d/100). The profit or loss percent is simply (SP − 100).
Micro-example: Markup 20%, discount 10%. SP = 100 × 1.2 × 0.9 = 108. Profit = 8%. No separate formula for profit%, no ratio setup. Standard method requires computing MP, then SP, then (SP−CP)/CP: 5 steps. Chain method: 2 steps. Time: 45s → 12s.
For exactly two years, avoid expanding (1 + r/100)² algebraically. Just multiply twice: Year 1 = Initial × (1 + r/100), Year 2 = Year 1 × (1 + r/100). For 5% growth on 80,000: 80,000 × 1.05 = 84,000; 84,000 × 1.05 = 88,200. Faster than squaring because the numbers stay clean. Formula expansion: 4 arithmetic operations. Step-by-step: 2 multiplications of similar difficulty. Speed: roughly equal, but step-by-step has lower error rate.
Read the question and locate the base first — every percentage is "of" something. Write it down explicitly before touching numbers.
Decision tree:
Single percentage of a number? → Direct: (P/100) × X. Use fraction equivalents from memory if P is 12.5, 16.67, 33.33, 66.67.
Comparison ("A is X% more/less than B")? → Write A = B × (1 ± X/100). If the question then asks "B is what % of A", the base has shifted — recompute from B/A × 100.
Two successive percentage changes? → Use net-change formula: a + b + ab/100 with signs. Verify sign of ab term (both positive = positive, one negative = negative).
Price-consumption / salary-savings inverse problem? → Use r/(100 ± r) × 100 template. Sign: +r in denominator if original variable increased, -r if decreased.
Mixture / concentration problem? → Set up the single equation: (existing amount + added) / (existing volume + added) = target %. Solve for the unknown.
Markup + discount? → Set CP = 100, chain multipliers, read profit/loss off SP directly.
If you cannot slot the question into one of these six types within 10 seconds, take CP = 100 or the given base value as your starting number and work forwards numerically. Do not get stuck in algebra.
Why this question: Tests the most basic salary comparison — confirms you know which is the base.
Solving path: B = ₹4800. A = 4800 + 25% of 4800 = 4800 + 1200 = ₹6000. The base is B's salary, not A's. One-line calculation.
Why this question: Mixture-concentration problems appear regularly and catch candidates who set up the wrong denominator.
Solving path: Existing alcohol = 20% of 500 = 100 ml. Let x ml of pure alcohol be added. Equation: (100 + x)/(500 + x) = 40/100. Cross-multiply: 250(100 + x) = 100(500 + x) — wait, simplify as 100 + x = 0.4(500 + x) → 100 + x = 200 + 0.4x → 0.6x = 100 → x = 166.67 ml. Confirm: (100 + 166.67)/(500 + 166.67) = 266.67/666.67 = 40%. Correct.
Why this question: The "P% of A = Q% of B" format is a staple in CGL and can be solved in one step with fraction recognition.
Solving path: 40% of 250 = 100. So 20% of x = 100, meaning x/5 = 100, so x = 500. Fraction approach: 40% = 2/5, so 2/5 × 250 = 100. Then 20% = 1/5, so x/5 = 100, x = 500. Under 10 seconds.
Why this question: Two-year growth at a fixed rate — confirms correct compounding (not simple addition of 5% + 5%).
Solving path: Year 1: 80,000 × 1.05 = 84,000. Year 2: 84,000 × 1.05 = 88,200. The wrong answer (88,000) would result from simple-interest-style thinking: 80,000 + 2 × 4,000 = 88,000. Compounding adds the extra 200.
Why this question: Successive percentage change — the most frequently tested percentage sub-type in SSC CGL.
Solving path: Use net-change formula: a = +20, b = -15. Net = 20 + (-15) + (20 × (-15)/100) = 5 - 3 = 2% increase. Or numerically: 100 → 120 → 120 × 0.85 = 102. Net change = +2%.
Why this question: Classic inverse percentage — tests whether you recognize the base has changed from original price to new price.
Solving path: Price rises 25%, so new price = 125. Expenditure = Price × Consumption. For expenditure to stay at 100 (old price × old consumption = 100 × 1 = 100), new consumption = 100/125 = 0.8. Reduction = 20%. Formula: 25/(100+25) × 100 = 25/125 × 100 = 20%.
Why this question: Markup plus discount — the chain multiplier approach saves time and avoids a common step-skipping error.
Solving path: Set CP = 100. Marked price = 100 × 1.20 = 120. After 10% discount: SP = 120 × 0.90 = 108. Profit = 108 − 100 = 8%. So net profit = 8%. Do not add or subtract the percentages directly (20% − 10% ≠ 10%; the base shifts).
Reversing the base in "A is X% more than B" questions. When the question follows up with "B is what % less than A?", candidates write X% again. The base has shifted to A. Always recompute using the new denominator.
Adding successive percentages directly. A 20% increase followed by a 15% decrease is not a 5% increase. The second percentage acts on the already-changed value. Use the net-change formula or compute numerically with 100 as base.
Using new price (not original) as the denominator in percentage change. The formula is (Change / Original) × 100. Putting the new value in the denominator is the single most common calculation error in this topic.
Confusing "percentage points" with "percentage change." If a rate moves from 20% to 25%, it has increased by 5 percentage points, but the percentage change in the rate is 5/20 × 100 = 25%. SSC CGL occasionally tests this distinction explicitly.
Mixture setup with wrong denominator. When you add x ml of pure substance, the new total volume is (original + x), not original. Forgetting to update the denominator gives a wrong equation.
Two-year growth calculated as simple interest. 80,000 × 5% × 2 = 8,000, giving 88,000 — wrong. Compound growth requires applying the multiplier twice: 80,000 × 1.05 × 1.05 = 88,200. The 200 difference is exactly the "interest on interest" that simple-interest thinking misses.