Percentage means "per hundred" — that is all it is. When you say 40%, you are saying 40 out of every 100 parts. The word comes from Latin "per centum", but for the exam, think of it this way: percentage is just a fraction with denominator 100, written in a more convenient form.
40% = 40/100 = 2/5
Here is the analogy that makes it stick. Imagine a CRPF platoon of 100 soldiers. If 45 are from rural areas, that is 45% rural. If the platoon had 200 soldiers and 90 are rural, it is still 45% — the ratio stays the same regardless of the actual count. That is the whole point of percentage: it standardises comparison across different totals.
Three things you will calculate in every percentage problem:
The third type trips up more SSC GD aspirants than the first two combined. You will see it in training-camp and security-force problems: "220 trainees are from urban areas, which is 55% of the total — find the total." The formula is simply:
Base = (Given Value / Given Percentage) × 100
One more foundational idea: percentage change. If something goes from an old value to a new value:
Percentage Change = [(New − Old) / Old] × 100
Positive result means increase, negative means decrease. This formula drives at least half the percentage questions on SSC GD.
You save 5–8 seconds per question if you already know these without calculating:
| Fraction | Percent | |----------|---------| | 1/2 | 50% | | 1/3 | 33.33% | | 1/4 | 25% | | 1/5 | 20% | | 1/6 | 16.67% | | 1/7 | 14.28% | | 1/8 | 12.5% | | 1/9 | 11.11% | | 1/10 | 10% | | 3/4 | 75% | | 2/3 | 66.67% | | 3/5 | 60% |
And their reverses: if price increases by 25% (= 1/4), consumption must decrease by 20% (= 1/5). Why 1/5? Because 1/4 ÷ (1 + 1/4) = (1/4)/(5/4) = 1/5. This relationship is the engine behind the price-consumption problem type.
When expenditure is fixed: Price × Consumption = Expenditure = Constant
So if price increases by r%, consumption must decrease by r/(100+r) × 100%.
If price decreases by r%, consumption can increase by r/(100−r) × 100%.
Look — these two formulas are inverses of each other. For the exam, just remember:
20/120 × 100 = 16.67%20/80 × 100 = 25%The PYQ on sugar (price down 20%, consumption up 25%) is a direct application. Don't derive it in the hall — know it.
When a value changes by a% first, then by b%:
Net change = a + b + (ab/100)%
This is the most important formula in percentage for SSC GD. It works for any combination:
Example: Salary up 15%, then down 10%.
Net = 15 + (−10) + (15 × −10)/100 = 15 − 10 − 1.5 = 3.5% increase
This matches the PYQ answer directly. No need to assume 100 and calculate step by step — though assuming 100 is a reliable fallback if you forget the formula.
Example: Population up 20%, then down 10%.
Net = 20 + (−10) + (20 × −10)/100 = 20 − 10 − 2 = 8% increase
Again, matches the PYQ.
This appears as "shopkeeper" problems. The chain is:
Cost Price → (Mark-up%) → Marked Price → (Discount%) → Selling Price
Profit% = [(SP − CP)/CP] × 100
For the mark-up 40%, discount 15% PYQ:
Or use the successive formula treating markup as +40 and discount as −15:
Net = 40 − 15 + (40 × −15)/100 = 25 − 6 = 19%
Same answer, two fewer arithmetic steps.
Pattern: "X% of total = some given number. Find total."
Formula: Total = Given Number / (X/100) = Given Number × (100/X)
For the border security force PYQ: unmarried = 72%, and 360 are unmarried.
Total = 360 × (100/72) = 360 × (25/18) = 500
Speed tip: convert 100/72 to its simplest fraction first (25/18), then multiply. Avoids decimal division.
When price changes by a fraction, flip the fraction for the consumption change. Price up by 1/5 (20%) → consumption down by 1/6 (16.67%). Price down by 1/5 (20%) → consumption up by 1/4 (25%). Rule: if price goes UP by p/q, consumption goes DOWN by p/(q+p). If price goes DOWN by p/q, consumption goes UP by p/(q−p). This takes 5 seconds once you know the fractions. Standard algebraic derivation: 30–40 seconds.
For two successive percentage changes a and b: Net% = a + b + ab/100. Write it as a + b + (product/100). For SSC GD problems, a and b are usually under 30, so the product/100 is a small integer or simple decimal. Example: 15% up then 10% down → 15 − 10 − 1.5 = 3.5%. Assuming base = 100 and computing in two steps: 5–6 steps total. Using formula: 3 arithmetic operations. Saves 15–20 seconds per problem.
When you see a reverse percentage (find total given a part and its %), first convert the percentage to a fraction. 45% → 9/20, 55% → 11/20, 72% → 18/25. Then divide the given number by that fraction (i.e., multiply by its reciprocal). This avoids messy decimal division. For 72% = 360: total = 360 × (25/18) = 500. Decimal method: 360 ÷ 0.72 requires long division. Fraction method: one multiplication. Saves 20–25 seconds.
Treat markup as +a% and discount as −b%. Apply successive formula: Net profit% = a − b − ab/100. Example: markup 40%, discount 15% → 40 − 15 − 6 = 19%. No need to assume CP = 100 and do two multiplications. Reduces 4 steps to 2 steps. Standard method: ~45 seconds. Successive formula: ~15 seconds.
When you see "3/5 of [number]", do not convert to percentage. Just multiply by 3 and divide by 5 directly. "3/5 of 1450" → 1450 ÷ 5 = 290, then 290 × 3 = 870. Tried via percentage (60% of 1450 = 1450 × 0.6): requires decimal multiplication, one extra step. Fraction route: 2 steps, both integer arithmetic. Saves 10–12 seconds.
In the exam hall, classify every percentage question in under 5 seconds:
Step 1 — Identify the question type:
Total = Given ÷ (Percent/100).a + b + ab/100.Step 2 — Choose numbers:
Step 3 — Compute and verify:
If two answer options are close (like 19% and 21%), re-check your ab/100 term — that is where errors happen.
Why this question: Tests combined operations — fraction of a number plus reverse percentage of 200%. A two-step problem that looks harder than it is.
Solving path: 3/5 of 1450 = 870. 200% of 450 = 900. So 870 + ? = 900, which gives ? = 30. The trap is treating "200% of 450" as 200, not 900. 200% means twice the value.
Why this question: Classic reverse percentage with a defence/paramilitary context. Knowing urban% from rural% is the key step.
Solving path: Rural = 45%, so Urban = 55%. Total = 220 ÷ 0.55 = 400. Fraction route: 220 × (20/11) = 400. Both work; fraction route avoids decimal division.
Why this question: Price-consumption inverse relationship — one of the most frequently tested percentage sub-types.
Solving path: Price down 20% → new price = 80. To spend the same 100, consumption = 100/80 = 1.25, a 25% increase. Or use the formula: decrease r% → consumption up r/(100−r)% = 20/80 × 100 = 25%.
Why this question: Markup and discount chain — tests whether you know profit is calculated on CP, not MP.
Solving path: CP = 100, MP = 140, SP = 140 × 0.85 = 119. Profit = 19%. Alternatively: successive formula → 40 − 15 − (40×15)/100 = 25 − 6 = 19%.
Why this question: Successive percentage change — border town population context, tests the +a−b−ab/100 formula.
Solving path: Net = 20 + (−10) + (20 × −10)/100 = 20 − 10 − 2 = 8% increase. Or: 100 → 120 → 108. Net change = 8%.
Why this question: Price-consumption with price increase — the mirror image of the sugar problem. Tests whether you know the different formula for price-up vs. price-down.
Solving path: Price up 25% → new price = 125. To maintain expenditure: 125 × new consumption = 100. New consumption = 80% of old → reduction = 20%. Formula: r/(100+r) = 25/125 = 1/5 = 20%.
Why this question: CRPF salary problem — another successive percentage. Tests that the order (up first, then down) matters and the formula handles the sign correctly.
Solving path: Net = 15 + (−10) + (15 × −10)/100 = 5 − 1.5 = 3.5% increase. Many aspirants just add 15 − 10 = 5% and pick "5% increase" — that ignores the interaction term ab/100.
Why this question: Reverse percentage with the complement — married vs. unmarried split. Tests whether you correctly identify which percentage corresponds to the given number.
Solving path: Married = 28%, so Unmarried = 72%. Total = 360 ÷ 0.72 = 500. Fraction: 360 × (100/72) = 360 × (25/18) = 500. Common error: using 28% instead of 72% for unmarried.
Confusing 200% of X with 200% more than X. "200% of 450" = 900. "200% more than 450" = 1350. These are different. In SSC GD questions, "200% of" almost always means multiply by 2, not add twice.
Using the wrong base in reverse percentage. If 28% are married and 360 are unmarried, the 360 corresponds to 72% (not 28%). Always ask: which group does the given number belong to, and what is that group's percentage?
Ignoring the interaction term in successive change. Net change is NOT simply a + b. It is a + b + ab/100. For 15% up and 10% down, writing 5% instead of 3.5% is the single most common error in this topic.
Calculating profit% on Marked Price instead of Cost Price. Profit percentage is always on Cost Price. If CP = 100 and SP = 119, profit% = 19%, not 19/140 × 100.
Applying the wrong formula for price-consumption direction. Price UP by r% → consumption DOWN by r/(100+r)%. Price DOWN by r% → consumption UP by r/(100−r)%. Swapping these two formulas flips your answer completely.
Not simplifying fractions before multiplying in reverse percentage. Doing 360 ÷ 0.72 as long division wastes 20+ seconds. Convert 0.72 to 18/25, flip to 25/18, multiply: 360 × 25/18 = 20 × 25 = 500. Always simplify first.