Percentage means "out of 100." The word itself comes from the Latin per centum — per hundred. When you say "40% of students passed," you mean 40 out of every 100 students passed. That is the whole idea.
Here is why this matters for SSC MTS specifically: percentage is not a standalone topic. It is the language that profit-loss, discount, simple interest, and election problems all speak. If you are shaky on percentage, every one of those chapters will feel like a foreign language. Get this right once, and you unlock five chapters simultaneously.
Think of percentage as a universal translator between fractions, decimals, and ratios. The number 0.25, the fraction 1/4, the ratio 1:4, and 25% are all saying the exact same thing in different dialects. Your job in the exam hall is to switch fluently between them.
The fundamental relationship:
Percentage = (Part / Whole) × 100
And working backwards: Part = (Percentage / 100) × Whole
An analogy that sticks: imagine a 100-slot parking lot. If 35 slots are occupied, 35% of the lot is full. If the lot had 200 slots and 70 were occupied, you still have 35% — because 70 out of 200 is the same ratio as 35 out of 100. Percentage always normalizes everything to a base of 100, which is why comparisons become easy.
One more thing before the deep dive: the "base" matters enormously. A 20% increase and a 20% decrease applied one after the other do not cancel each other out. They leave you with a net loss of 4%. This non-intuitive behavior trips up candidates on almost every mock. You will see exactly why in the next section.
Stop calculating these every time. Memorize the fraction equivalents and the exam becomes 30% faster:
| Percentage | Fraction | Decimal | | ---------- | -------- | ------- | | 10% | 1/10 | 0.1 | | 12.5% | 1/8 | 0.125 | | 16.67% | 1/6 | 0.167 | | 20% | 1/5 | 0.2 | | 25% | 1/4 | 0.25 | | 33.33% | 1/3 | 0.333 | | 37.5% | 3/8 | 0.375 | | 40% | 2/5 | 0.4 | | 50% | 1/2 | 0.5 | | 60% | 3/5 | 0.6 | | 66.67% | 2/3 | 0.667 | | 75% | 3/4 | 0.75 |
When you see "25% of 300," do not multiply 300 × 25/100. Instead think: 25% = 1/4, so 300/4 = 75. Done in 3 seconds.
Percentage Change = [(New Value - Old Value) / Old Value] × 100
If the result is positive, it is an increase. If negative, it is a decrease.
Critical point — the base always changes. A salary goes from Rs. 10,000 to Rs. 12,000. Increase = 2000/10,000 × 100 = 20%. Now it drops back from Rs. 12,000 to Rs. 10,000. The decrease = 2000/12,000 × 100 = 16.67%. Same absolute change, different percentage — because the base shifted.
When two successive percentage changes of a% and b% are applied:
Net Change% = a + b + (a × b)/100
Example: Price increases 20%, then decreases 20%. Net change = 20 + (–20) + (20 × (–20))/100 = 0 – 400/100 = –4%
So you end up 4% lower than where you started. The formula saves you from calculating step by step.
This is a classic SSC pattern. If price increases by r%, the reduction in consumption to maintain the same expenditure is:
Reduction% = r / (100 + r) × 100
Price up 25%: Reduction = 25/125 × 100 = 20%
Price up 20%: Reduction = 20/120 × 100 = 16.67%
Commit the formula and you solve these in under 10 seconds.
If someone spends x% of income, they save (100 – x)%. The three quantities are always locked in this relationship:
Savings = Income – Expenditure
Savings% = 100% – Expenditure%
So if expenditure is 75%, savings is 25%. If savings amount is given, the whole income = Savings × 100 / Savings%.
Passed in at least one = Passed in A + Passed in B – Passed in both
Failed in both = 100% – (Passed in at least one)
This is the inclusion-exclusion principle in percentage clothing. When you see a question about two subjects, two candidates, or two categories — always draw a mental Venn diagram and apply this.
If a% of x = b% of y, then:
x/y = b/a
Notice the flip: the percentages switch sides when you write the ratio. This is where almost everyone makes an error. If 30% of x = 25% of y, then x/y = 25/30 = 5/6.
When income-savings questions appear, directly use: Income = Savings × (100 / Savings%). In the question "saves Rs. 2000, spends 75%," savings% = 25%. So income = 2000 × (100/25) = 2000 × 4 = Rs. 8000. You never need to set up an equation. Standard algebraic method: ~40 seconds. This substitution: ~8 seconds.
When price rises by r%, consumption must fall by r/(100+r) × 100 percent to keep expenditure constant. For 25% rise: denominator = 125, answer = 25/125 × 100 = 20%. The denominator is always (100 + rise%). Once you see a "reduce consumption" question, write the denominator first, then divide. Standard equation method: ~50 seconds. Pattern method: ~12 seconds.
When a% of x = b% of y, the ratio x:y = b:a — the percentages flip. See 30% and 25%? The ratio is 25:30 = 5:6. No algebra needed. The switch works because both sides share the /100 factor which cancels, leaving ax = by, so x/y = b/a. Standard cross-multiplication: 4 steps. Pattern recognition: 1 step.
Mentally assign 100 students total for any exam/election question. Fill in the given percentages directly as numbers (60% of Math passers = 60 students). Passed in both = 40, so passed in at least one = 60 + 70 – 40 = 90. Failed both = 100 – 90 = 10 = 10%. You work with whole numbers, not percentages, which eliminates fraction arithmetic. Reduces error probability by roughly half compared to working purely in percentages throughout.
Let CP = 100 always. Mark up by 30% → MP = 130. Discount 20% on 130 → SP = 130 × 0.8 = 104. Profit = 4%. No formula needed — just two multiplications on the base 100. Setting CP = 100 removes one unknown, collapsing what looks like a two-variable problem into pure arithmetic. Standard method: ~60 seconds. Base-100 substitution: ~20 seconds.
When you see a percentage question in the exam, run this check in sequence:
Step 1 — Identify the question type:
Step 2 — Pick the base:
Step 3 — Solve with fractions, not decimals:
Step 4 — Sanity check:
For SSC MTS, most percentage questions resolve in under 30 seconds with the right framework. If you are taking longer than a minute, you are using the wrong approach — stop and switch.
Why this question: The most direct income-savings type. Tests whether you use the complement (savings%) correctly.
Solving path: Spends 75% → saves 25%. Savings amount = Rs. 2000 = 25% of income. Income = 2000 × (100/25) = 2000 × 4 = Rs. 8000. Done in one multiplication.
Why this question: The price-consumption trade-off is a recurring SSC MTS pattern. The trap is dividing 25 by 100 instead of by 125.
Solving path: New price base = 100 + 25 = 125. Reduction% = 25/125 × 100 = 20%. The denominator must be the new (increased) price, not the original.
Why this question: Tests whether you can find the "remainder" percentage in a multi-candidate election. SSC loves this type.
Solving path: Valid votes = 45 + 35 = 80%. Invalid = 20%. 20% of 8000 = 1600. Two steps, both trivial once you identify that invalid = 100 – valid.
Why this question: The fraction-switch trap — candidates almost always write the ratio in the wrong order.
Solving path: 30x = 25y (the /100 cancels). So x/y = 25/30 = 5/6. x:y = 5:6. Remember: the percentages flip when you write the ratio.
Why this question: Combines markup and discount in one question — common in SSC MTS and a direct test of the "Set CP = 100" technique.
Solving path: CP = 100. MP = 130. After 20% discount: SP = 130 × 80/100 = 104. Profit = 4%. The answer lands right on a round number, which is your confirmation that the approach is correct.
Why this question: Two-subject Venn diagram type — the inclusion-exclusion formula in percentage form. Tests conceptual clarity.
Solving path: Passed at least one = 60 + 70 – 40 = 90%. Failed both = 100 – 90 = 10%. No actual student numbers needed — the percentages are self-contained.
Why this question: Two-step percentage question where you first find the whole, then apply a new percentage to it. Tests sequential calculation accuracy.
Solving path: 25% of x = 75 → x/4 = 75 → x = 300. Then 40% of 300 = 120. Key: do not jump to 40% without first anchoring the base number.
Why this question: Multi-step calculation with subgroups. Tests whether you can hold two parallel calculations without mixing up the groups.
Solving path: Boys = 60% of 50 = 30. Girls = 50 – 30 = 20. Cricket (boys) = 20% of 30 = 6. Cricket (girls) = 25% of 20 = 5. Total = 11. Work each group separately; never mix percentages across groups.
Using the original price as the base for consumption reduction. When price rises by 25%, the reduction formula uses 125 (new price) as the denominator, not 100. Writing 25/100 × 100 = 25% is wrong. The correct answer is 20%.
Writing the ratio in the same order as the percentages. When 30% of x = 25% of y, beginners write x:y = 30:25. It is the reverse: x:y = 25:30. The cross-multiplication flips the sides.
Forgetting to subtract "both" in two-category problems. If 60% passed Maths and 70% passed Science with 40% in both, naively adding gives 130% — impossible. Always subtract the overlap.
Applying successive percentage changes by simply adding them. A 20% increase followed by a 20% decrease is not zero change. Use the formula a + b + ab/100 and you get –4%. Adding percentages directly only works if both changes apply to the same original base simultaneously.
Mixing up which number is "part" and which is "whole." In "saves Rs. 2000 and spends 75%," the Rs. 2000 is 25% of income, not 75%. Correctly identifying which percentage applies to which number is the first and most important step.
Computing 40% of a wrong base after a two-step problem. In questions like "25% of x = 75, find 40% of x," some candidates compute 40% of 75 instead of finding x first (= 300) and then computing 40% of 300. Always anchor the full value before applying a new percentage.