Percentage — SSC CGL Quantitative Aptitude

Percentage is not "a chapter" in SSC CGL — it is the language the entire arithmetic block speaks. Profit & loss is percentage applied to prices. Interest is percentage applied to time. Data Interpretation is percentage applied to charts. Learn to convert between fractions and percentages instantly, and questions that look like 90-second problems collapse into 15-second reads.

1. What SSC actually asks

Percentage contributes 1–2 direct questions in Tier 1 and 2–3 in Tier 2 (Mathematical Abilities) — but that undersells it. PYQ analyses consistently show 8–10 questions per paper that are percentage in disguise: profit-loss, discount, interest, alligation and nearly all of DI. SSC's favourite direct patterns:

1. Successive change — "a number is increased by 20% then decreased by 20%…"
2. Comparison — "A's income is 25% more than B's; B's is what % less than A's?"
3. Consumption–price — "price rises 25%; by what % must consumption fall so expenditure is unchanged?"
4. Population / machine value — growth and depreciation over 2–3 years.
5. Exam / election — "a candidate scores 33% and fails by 40 marks…", "one candidate gets 42% of votes and loses by 1,440 votes…"
6. Fraction-of-fraction — "40% of 60% of ⅚ of a number is…"

Every one of these has a template. This chapter gives you all six.

2. The percentage ↔ fraction toolkit (memorise first, everything else second)

"Per cent" means per hundred: $x\%=\frac{x}{100}$. The single biggest speed unlock in SSC quant is converting percentages to fractions before calculating:

Extensions come free: if $\frac{1}{8}=12.5\%$, then $\frac{3}{8}=37.5\%$ and $\frac{5}{8}=62.5\%$. If $\frac{1}{11}=9.09\%$, then $63.63\%=\frac{7}{11}$.

Why this matters: "Find 87.5% of 640" is painful as $\frac{87.5\times 640}{100}$ but trivial as $\frac{7}{8}\times 640=560$. SSC deliberately picks numbers that reward the fraction route.

The multiplying factor (MF)

Every percentage change is a single multiplication:

• +20% → multiply by $1.20$ (or $\frac{6}{5}$)
• −25% → multiply by $0.75$ (or $\frac{3}{4}$)

Never compute "the increase" separately and add it back. Go straight to the final value with one factor. This is the method every other arithmetic chapter builds on.

3. Successive percentage change

Two changes of $a\%$ and $b\%$ (use signs: increase +, decrease −) combine into one net change:

$\text{Net }\%=a+b+\frac{ab}{100}$

Example. Price rises 20%, then falls 20%. Net $=20-20+\frac{(20)(-20)}{100}=-4\%$ — a 4% fall, not zero. (This asymmetry is a permanent SSC trap.)

For three or more changes, chain multiplying factors: $+10\%,+20\%,-25\%$ → $1.1\times 1.2\times 0.75=0.99$ → net −1%.

Area version: if a rectangle's length changes by $a\%$ and breadth by $b\%$, the area changes by the same formula — because area is a product. A square's side up 30% → area up $30+30+9=69\%$.

4. The comparison template: "% more" vs "% less"

If A is $x\%$ more than B, then B is less than A by:

$\frac{x}{100+x}\times 100\%$

If A is $x\%$ less than B, then B is more than A by $\frac{x}{100-x}\times 100\%$.

The fraction route is faster. "A is 25% more than B" means $A=\frac{5}{4}B$ — so B is $\frac{4}{5}$ of A, i.e. $\frac{1}{5}=20\%$ less. Convert the percentage to a ratio, flip it, read the answer.

This same identity powers the consumption–price template: price up $25\%=\frac{1}{4}$ → consumption must fall by $\frac{25}{125}=\frac{1}{5}=20\%$ to keep expenditure constant.

5. Growth & depreciation (population, machines, salaries)

Growth at $r\%$ per period for $n$ periods:

$\text{Final}=\text{Initial}{\left(1+\frac{r}{100}\right)}^n\text{Depreciation: }{\left(1-\frac{r}{100}\right)}^n$

Example. A town of 8,000 grows 5% yearly for 2 years: $8000\times {\left(\frac{21}{20}\right)}^2=8000\times \frac{441}{400}=8820$.

Notice the move: $1.05=\frac{21}{20}$, and 8000 divides cleanly by $400=20^2$. SSC numbers are engineered for the fraction route — if your arithmetic is getting ugly, you've missed the intended fraction.

Different rates each year? Chain the factors: $\left(1+\frac{r_1}{100}\right)\left(1+\frac{r_2}{100}\right)\dots$

6. Exam-marks and election templates

Pass-fail: A candidate scoring 33% fails by 40 marks; another scoring 45% gets 56 more than pass marks. Then the gap between their scores, $45\%-33\%=12\%$ of total, equals $40+56=96$ marks. So total $=96÷0.12=800$, and pass marks $=0.33\times 800+40=304$.

The template: the difference in percentages always equals the difference in marks. One line: $(p_2-p_1)\%\times T=m_1+m_2$.

Two-candidate election: winner gets 56% of valid votes and wins by 1,440. The margin is $56\%-44\%=12\%$ of valid votes → valid votes $=1440÷0.12=12,000$. If some votes are invalid, peel that layer first (invalid % applies to total votes).

7. Fraction-of-fraction chains

"What is 40% of 60% of $\frac{5}{6}$ of 3,000?"

$\frac{2}{5}\times \frac{3}{5}\times \frac{5}{6}\times 3000=\frac{2\times 3\times 5\times 3000}{5\times 5\times 6}=600$

Convert everything to fractions, cancel ruthlessly, multiply what survives. Never compute intermediate percentages — cancellation is the whole point.

8. Solved PYQ-style examples

Q1 (Tier-1 pattern). If 60% of a number is 36 more than 40% of the same number, the number is? Solution. The gap $60\%-40\%=20\%$ equals 36 → number $=36\times 5=180$. (One line: a percentage gap IS the quantity gap.)

Q2 (Tier-1 pattern). A's salary is 50% more than B's. B's salary is what per cent less than A's? Solution. $A=\frac{3}{2}B\Rightarrow B=\frac{2}{3}A$ → B is $\frac{1}{3}\approx 33.33\%$ less. (Flip the fraction, don't re-derive.)

Q3 (Tier-2 pattern). The price of sugar falls 10%, so a family buys 5 kg more for ₹270. The original price per kg? Solution. Money saved on the original quantity = 10% of 270 = ₹27; this buys the extra 5 kg at the new price → new price = 27/5 = ₹5.40 → original price $=5.40÷0.9=₹6$.

Q4 (Tier-2 pattern). In an exam 52% failed in English, 42% in Maths and 17% in both. What % passed in both? Solution. Failed in at least one $=52+42-17=77\%$ → passed both $=23\%$. (Set-union in percentage clothing — see the Venn Diagrams chapter.)

Q5 (trap check). A number is first increased by 25% and the result decreased by 25%. Net effect? Solution. $+25-25+\frac{25\times (-25)}{100}=-6.25\%$. Down, always down — a symmetric up-down always ends below start.

9. The 36-second protocol

Tier 1 gives you 15 minutes for 25 quant questions — 36 seconds each. For percentage questions:

1. Read the last line first — what is actually asked (% or value? of what base?).
2. Convert every % to a fraction as you read.
3. Reach for the template (successive / comparison / consumption / growth / exam / election).
4. If the numbers turn ugly, you picked the wrong base — re-read "per cent of what".