SSC CGL Maths · Data Interpretation

Percentage Change and Percent More or Less

A percentage change, or a "percent more than", is the difference divided by the base, and the base is the earlier value or the value after the word "than".

All Data Interpretation notes

Why this matters

Twenty-three questions in the bank, nine of them MODERATE. Every wrong option in these is a wrong base: the same difference divided by the other value. Fix the base before you divide and the rest is one line.

Concept 1 of 3: Percentage increase or decrease between two values

A change is measured against where you started. Going from 40 to 50 is a rise of 10 on a start of 40, which is 25%. Coming back from 50 to 40 is the same 10 on a start of 50, only 20%. The start is the earlier year, or the year after "compared with" or "over".

Definition

Full method: $\frac{\text{new} - \text{old}}{\text{old}} \times 100$ . A negative answer is a decrease; quote it without the sign as "percentage decrease".
Old value: the earlier year, "the previous year", or the value after "compared with".
Fast route: write new $\div$ old as a fraction. $\frac{5}{4}$ is a 25% rise, $\frac{3}{4}$ a 25% fall, doubling is a 100% rise.
Which change is largest in percentage: compare change $\div$ old for each item. The largest change in units is not always the largest in percent, because a small base inflates the percentage.
A table can print the yearly percentages themselves; then "percentage increase from 70 to 84" is still $\frac{14}{70} = 20\%$ , a change measured on the printed numbers.

Percentage change

\%\,\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100

Worked example

The table shows a factory's monthly output of bulbs.

Month	March	April	May	June
Bulbs	640	600	560	512

What is the percentage decrease in output in June compared with March?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 23 Sep 2024, Shift 3 · Q55Easy

Example 1 · Data Interpretation · Percentage Change and Percent More or Less

The monthly production of electric bulbs by a company during the second half of the year 2021 is shown by the following bar graph. Study the bar graph carefully and answer the question given below. What is the percentage decrement in the production of electric bulbs in October as compared to the production in July? (Correct up to two decimal places.)

Dividing by the new value

A rise from 40 to 50 is 25%, not 20%. The change is always divided by the starting value; dividing by the later value gives a smaller, wrong answer that sits among the options.

Taking the biggest jump as the biggest percentage

A rise of 36 on a base of 60 is 60%, while a rise of 21 on a base of 28 is 75%. Compare change over base, not the changes alone.

Drill 13 more on percentage increase or decrease between two values

Concept 2 of 3: Percent more than and percent less than

"A is what percent more than B" measures the gap against B, the value after "than". Turn it round and ask how much less B is than A, and the gap is now measured against A, so the percentage is smaller. The two answers are never equal.

Definition

A more than B: $\frac{A - B}{B} \times 100$ . A less than B: $\frac{B - A}{B} \times 100$ . The base is the value after "than".
More/less options: first decide the direction (is A bigger?), then work out the size.
Turning it round: if A is $r\%$ more than B, then B is $\frac{r}{100 + r} \times 100\%$ less than A. 25% more one way is 20% less the other way.
Averages over the same count: compare the totals; the divisions cancel.

Percent more or less

\frac{A - B}{B} \times 100 \qquad A = B\left(1 + \frac{r}{100}\right) \Rightarrow B \text{ is } \frac{r}{100 + r} \times 100\% \text{ less than } A

Worked example

Plant P made 2,760 units and plant Q made 2,400 units. By what percent is P's output more than Q's? By what percent is Q's output less than P's?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 12 Sep 2024, Shift 1 · Q68Easy

Example 2 · Data Interpretation · Percentage Change and Percent More or Less

The given table shows the number of soaps sold by four different companies in 4 different months.

Company / Month	May	June	July	August
P	1924	1780	1820	1490
Q	1540	1245	1648	2450
R	2035	1485	1350	1650
S	1736	1855	1470	1180

The total number of soaps sold by companies Q and S together in May, is what percentage more than the number of soaps sold by company P in July?

Using the same percentage both ways

If A is 25% more than B, B is not 25% less than A. The gap is measured on different bases, so B is 20% less than A.

Picking the size before the direction

More/less questions print each size twice, once with "more" and once with "less". Decide which value is bigger before you divide.

Drill 4 more on percent more than and percent less than

Concept 3 of 3: Applying a percentage change to find a value

Sometimes the percentage is given and the value is asked: next year is 15% more than this year, income is expenditure plus a profit percentage. Multiply by one plus the rate. To go back from the new value, divide by the same factor.

Definition

Increase by $r\%$ : new $=$ old $\times (1 + \frac{r}{100})$ . Decrease by $r\%$ : new $=$ old $\times (1 - \frac{r}{100})$ .
Profit on expenditure: profit $=$ expenditure $\times \frac{p}{100}$ ; income $=$ expenditure $\times (1 + \frac{p}{100})$ .
Back to the old value: old $=$ new $\div (1 + \frac{r}{100})$ . Taking $r\%$ off the new value is wrong.
Fast route: split the rate into easy parts. 12.5% of 2,400 is $\frac{1}{8}$ of it, 300.

Applying a percentage change

\text{New} = \text{Old} \times \left(1 + \frac{r}{100}\right) \qquad \text{Old} = \frac{\text{New}}{1 + \frac{r}{100}}

Worked example

A company spent ₹36 crore in a year and made a profit of 35% on its expenditure. Taking income as expenditure plus profit, find its income.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 9 Sep 2024, Shift 3 · Q52Easy

Example 3 · Data Interpretation · Percentage Change and Percent More or Less

The given table shows the number of pages printed by four printers in three days.

Days	L	M	N	O
Friday	10,230	9580	7560	9600
Saturday	8540	11,230	6580	7890
Sunday	9235	8264	7546	10,325

If the total number of pages printed by all the given printers together on Wednesday was

15\%

more than the total number of pages printed by all the given printers together on Saturday, what was the total number of pages printed by all the

Taking the percentage off the new value

If 32,400 is 8% more than last year, last year is

32400 \div 1.08 = 30000

, not

32400 - 8\%

of 32,400. The 8% belongs to last year's value.

Drill 3 more on applying a percentage change to find a value

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 increase or decrease between two values
Percentage change
$\%\,\text{change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100$
Percent more than and percent less than
Percent more or less
$\frac{A - B}{B} \times 100 \qquad A = B\left(1 + \frac{r}{100}\right) \Rightarrow B \text{ is } \frac{r}{100 + r} \times 100\% \text{ less than } A$
Applying a percentage change to find a value
Applying a percentage change
$\text{New} = \text{Old} \times \left(1 + \frac{r}{100}\right) \qquad \text{Old} = \frac{\text{New}}{1 + \frac{r}{100}}$

Watch out for (5)

Dividing by the new value
→ Percentage increase or decrease between two values
Taking the biggest jump as the biggest percentage
→ Percentage increase or decrease between two values
Using the same percentage both ways
→ Percent more than and percent less than
Picking the size before the direction
→ Percent more than and percent less than
Taking the percentage off the new value
→ Applying a percentage change to find a value

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