SSC CGL Maths · Percentage, Profit and Loss

Percentage Basics

A percentage is a fraction with 100 at the bottom: x% of a number is x hundredths of it, and every percentage is measured against a base.

All Percentage, Profit and Loss notes

Why this matters

31 questions in the bank, 29 of them EASY and 22 from 2025 alone. They are one-line sums (a percentage of a number, the whole from a part, a ratio from equal percentages, more than and less than), so they are the marks to bank in under 30 seconds each. Speed comes from knowing the common percentages as fractions.

Concept 1 of 4: Percentage of a quantity and finding the whole

Per cent means 'out of 100'. So 35% of something is 35 parts in every 100 parts of it. If you know the size of a part and its percentage, you can scale back up to the whole.

Definition

$x\%$ of $N$ is $\frac{x}{100} \times N$ .
If $x\%$ of a whole is $A$ , the whole is $\frac{A \times 100}{x}$ .
Shares of the same whole add up to $100\%$ . If 30% and 45% are used, 25% is left.
Fast route: $10\%$ is the number with the decimal point moved one place, $1\%$ two places. Build any percentage from these: $35\% = 10\% + 10\% + 10\% + 5\%$ .
Put both amounts in the same unit before you divide (litres with litres, paise with paise).

Part and whole

x\% \text{ of } N = \frac{x}{100} \times N \qquad \text{whole} = \frac{\text{part} \times 100}{x}

Worked example

A school has 640 students and 35% of them come by bus. How many students come by bus?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 26 Sep 2025, Shift 3 · Q57Easy

Example 1 · Percentage, Profit and Loss · Percentage Basics

A man spends 30% of his salary on rent, 20% on groceries, and 25% on other expenses. If he saves Rs. 9,000, what is his salary?

Answering the part that was given

When a question asks for the part left over (empty, saved, spent on other things), take the given shares away from 100% first. A 5 L can holding 4 L is 80% full, so the empty share asked for is 20%.

Mixing units

A percentage compares like with like. 0.002 kilolitres is 2,000 millilitres, so change every amount to one unit before dividing.

Drill 9 more on percentage of a quantity and finding the whole

Concept 2 of 4: Common percentages as fractions

SSC numbers are chosen to divide cleanly by a friendly fraction.

12\frac{1}{2}\%

of 720 is just

720 \div 8 = 90

, one step instead of a long multiplication. Learn this table both ways and most percentage sums become a single division.

Definition

A percentage with a fraction in it, such as $33\frac{1}{3}\%$ , is almost always a simple fraction in disguise.
Build new ones from the table: $37\frac{1}{2}\% = 3 \times 12\frac{1}{2}\% = \frac{3}{8}$ , and $83\frac{1}{3}\% = 5 \times 16\frac{2}{3}\% = \frac{5}{6}$ .
Keep recurring ones as fractions until the last step; rounding early gives a wrong option.

Fraction	Percentage
$\frac{1}{2}$	$50\%$
$\frac{1}{3}$	$33\frac{1}{3}\%$
$\frac{2}{3}$	$66\frac{2}{3}\%$
$\frac{1}{4}$	$25\%$
$\frac{1}{5}$	$20\%$
$\frac{1}{6}$	$16\frac{2}{3}\%$
$\frac{1}{7}$	$14\frac{2}{7}\%$
$\frac{1}{8}$	$12\frac{1}{2}\%$
$\frac{3}{8}$	$37\frac{1}{2}\%$
$\frac{5}{8}$	$62\frac{1}{2}\%$
$\frac{1}{9}$	$11\frac{1}{9}\%$
$\frac{1}{11}$	$9\frac{1}{11}\%$
$\frac{1}{12}$	$8\frac{1}{3}\%$ Easy to confuse with one eighth, which is 12½%.
$\frac{1}{16}$	$6\frac{1}{4}\%$
$\frac{1}{20}$	$5\%$
$\frac{1}{25}$	$4\%$

To use a row, divide by the bottom of the fraction and multiply by the top.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 12 Sep 2025, Shift 3 · Q61Easy

Example 2 · Percentage, Profit and Loss · Percentage Basics

Evaluate:

12\left(\frac{1}{2}\right)\%

of 560 km +

66\left(\frac{2}{3}\right)\%

of 240 km

Rounding a recurring percentage too early

33\%

of 900 is 297, but

33\frac{1}{3}\%

of 900 is exactly 300. Use the fraction

\frac{1}{3}

, not 33.

Drill 1 more on common percentages as fractions

Concept 3 of 4: Equal percentages of two numbers give their ratio

If 40% of A is the same as 24% of B, then A must be the smaller number: it takes a bigger share of A to match a smaller share of B. The two percentages, swapped, give the ratio.

Definition

From $\frac{a}{100}A = \frac{b}{100}B$ we get $A : B = b : a$ .
For three numbers with $a\%$ of A $=$ $b\%$ of B $=$ $c\%$ of C, set each equal to 1. Then $A = \frac{100}{a}$ , $B = \frac{100}{b}$ , $C = \frac{100}{c}$ , and clear the fractions.
A difference of two percentages of the same number is one percentage: $x\%$ of N minus $y\%$ of N is $(x - y)\%$ of N.
With brackets such as 25% of $(P + Q)$ , multiply out, collect P on one side and Q on the other, then read the ratio.

Equal percentages and differences

a\% \text{ of } A = b\% \text{ of } B \implies A : B = b : a \qquad x\% \text{ of } N - y\% \text{ of } N = (x - y)\% \text{ of } N

Worked example

If 40% of A is equal to 24% of B, find A : B.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 1 · Q52Easy

Example 3 · Percentage, Profit and Loss · Percentage Basics

25\%

of A =

20\%

of B =

10\%

of C, find A : B : C.

Writing the ratio the wrong way round

When 40% of A equals 24% of B, A is the smaller number, so A : B is 24 : 40, which is 3 : 5. Writing 40 : 24 gives the reverse ratio, and SSC prints it as an option.

Drill 8 more on equal percentages of two numbers give their ratio

Concept 4 of 4: More than, less than and the changing base

Every percentage is measured against a base: the number after 'than' or 'of'. If Rahul earns 25% more than Sumit, the base is Sumit's pay. Turn the sentence around and the base becomes Rahul's pay, which is bigger, so the percentage gets smaller.

Definition

'A is r% more than B' means $A = B\left(1 + \frac{r}{100}\right)$ .
Then B is less than A by $\frac{r}{100 + r} \times 100\%$ .
'A is r% less than B' makes B more than A by $\frac{r}{100 - r} \times 100\%$ .
Fast route: call the base 100. If B is 100, A is 125; the gap of 25 out of 125 is 20%.
Fraction route: a rise of $\frac{1}{n}$ is undone by a fall of $\frac{1}{n + 1}$ . A rise of $\frac{1}{4}$ (25%) needs a fall of $\frac{1}{5}$ (20%).
For a chain (A more than B, B more than C), call the last one 100 and walk up the chain one step at a time.

Turning a comparison around

\text{less by } \frac{r}{100 + r} \times 100\% \qquad \text{more by } \frac{r}{100 - r} \times 100\%

rthe percentage in the original comparison

Worked example

Rahul earns 25% more than Sumit. By what percentage does Sumit earn less than Rahul?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 21 Sep 2025, Shift 3 · Q62Moderate

Example 4 · Percentage, Profit and Loss · Percentage Basics

A number was mistakenly increased by 25% instead of decreased by 20%. By what percent is the final result more than the CORRECT value?

Using the same percentage both ways

If A is 20% more than B, B is not 20% less than A. With B = 100 and A = 120, B is 20 less on a base of 120, which is

16\frac{2}{3}\%

Comparing against the wrong number

In 'by what per cent is the wrong result more than the correct one', the base is the correct result. A wrong 150 against a correct 120 is 25% more, not 20%.

Drill 9 more on more than, less than and the changing base

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Percentage of a quantity and finding the whole
Part and whole
$x\% \text{ of } N = \frac{x}{100} \times N \qquad \text{whole} = \frac{\text{part} \times 100}{x}$
Equal percentages of two numbers give their ratio
Equal percentages and differences
$a\% \text{ of } A = b\% \text{ of } B \implies A : B = b : a \qquad x\% \text{ of } N - y\% \text{ of } N = (x - y)\% \text{ of } N$
More than, less than and the changing base
Turning a comparison around
$\text{less by } \frac{r}{100 + r} \times 100\% \qquad \text{more by } \frac{r}{100 - r} \times 100\%$

Reference tables (1)

Common percentages as fractions16 rows

Fraction	Percentage
$\frac{1}{2}$	$50\%$
$\frac{1}{3}$	$33\frac{1}{3}\%$
$\frac{2}{3}$	$66\frac{2}{3}\%$
$\frac{1}{4}$	$25\%$
$\frac{1}{5}$	$20\%$
$\frac{1}{6}$	$16\frac{2}{3}\%$
$\frac{1}{7}$	$14\frac{2}{7}\%$
$\frac{1}{8}$	$12\frac{1}{2}\%$
$\frac{3}{8}$	$37\frac{1}{2}\%$
$\frac{5}{8}$	$62\frac{1}{2}\%$
$\frac{1}{9}$	$11\frac{1}{9}\%$
$\frac{1}{11}$	$9\frac{1}{11}\%$
$\frac{1}{12}$	$8\frac{1}{3}\%$ Easy to confuse with one eighth, which is 12½%.
$\frac{1}{16}$	$6\frac{1}{4}\%$
$\frac{1}{20}$	$5\%$
$\frac{1}{25}$	$4\%$

To use a row, divide by the bottom of the fraction and multiply by the top.

Watch out for (6)

Answering the part that was given
→ Percentage of a quantity and finding the whole
Mixing units
→ Percentage of a quantity and finding the whole
Rounding a recurring percentage too early
→ Common percentages as fractions
Writing the ratio the wrong way round
→ Equal percentages of two numbers give their ratio
Using the same percentage both ways
→ More than, less than and the changing base
Comparing against the wrong number
→ More than, less than and the changing base

Test yourself on Percentage, Profit and Loss

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

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