SSC CGL Maths · Data Interpretation

One Value as a Percentage of Another

"A is what percent of B" is A divided by B, times 100, and the value after the word "of" is always the base.

Why this matters

Thirty-four questions in the bank, and fifteen of them are MODERATE, the most of any page in this chapter. The options sit a fraction of a percent apart (94.92%, 94.95%, 94.98%), so a known fraction or a quick 1% estimate is what finishes these inside the time.

Concept 1 of 4: One value as a percentage of another

A percentage answers "how many for every hundred of the base". Divide the value by the base and scale to 100. The base is whatever comes after "of" or "compared with"; the answer can be more than 100% when the value is bigger than the base.

Definition

Full method: $\frac{A}{B} \times 100$ , where B follows the word "of".
Fast route by 1%: find 1% of B (move the decimal two places), then ask how many of those fit into A. For 384 of 1280: 1% is 12.8 and $384 \div 12.8 = 30$ .
Fast route by fractions: reduce $\frac{A}{B}$ first; a known fraction gives the percentage at once (the next concept lists them).
Averages over the same count: A's average as a percentage of B's average is A's total as a percentage of B's total.
Above 100%: 2.25 times the base is 225%. Split it as $200\% +$ the rest when the options differ only in the hundreds.
Round only at the end, to the places the question asks for.

A as a percentage of B

\frac{A}{B} \times 100\%

Athe value being described
Bthe base, the value after "of"

Worked example

The table shows a company's expenses (in ₹ lakh) over four years.

Year	Salary	Tax
2019	290	84
2020	310	92
2021	330	98
2022	350	110

The total tax over the four years is what percentage of the total salary?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 10 Sep 2024, Shift 3 · Q51Moderate

Example 1 · Data Interpretation · One Value as a Percentage of Another

The table below shows incomes (in rupees) earned by five employees of a company during the month of March 2019 and the income sources.

Source/Name of Employee	Reeta	Seeta	Geeta	Neeta	Aneeta
Overtime	2,500	2,800	2,300	2,200	2,600
Arrears	4,500	4,800	4,900	5,300	5,600
Bonus	2,300	2,100	2,500	2,700	2,800
Salary	24,000	30,000	29,000	32,000	34,000

The total amount of arrears paid by the company during the given period is what percentage of the total amount of bonus paid during the given period?

Dividing by the wrong base

"A is what percent of B" divides by B. Swapping them gives a number on the other side of 100%, and that number is usually one of the options.

Drill 13 more on one value as a percentage of another

Concept 2 of 4: Fractions and their percentage values

Many data questions are built so that the two totals reduce to a simple fraction. If you know these values by heart,

\frac{350}{400} = \frac{7}{8}

is 87.5% the moment you see it, with no long division.

Definition

Reduce the fraction first (divide top and bottom by a common factor), then read its value from the table. A multiple of a listed fraction is the same multiple of its percentage: $\frac{3}{16} = 3 \times 6.25\% = 18.75\%$ .

Fraction	Percentage	Fraction	Percentage
$\frac{1}{2}$	50%	$\frac{1}{8}$	12.5%
$\frac{1}{3}$	33.33%	$\frac{3}{8}$	37.5%
$\frac{2}{3}$	66.67%	$\frac{5}{8}$	62.5%
$\frac{1}{4}$	25%	$\frac{7}{8}$	87.5%
$\frac{3}{4}$	75%	$\frac{1}{9}$	11.11%
$\frac{1}{5}$	20%	$\frac{1}{11}$	9.09%
$\frac{1}{6}$	16.67%	$\frac{1}{12}$	8.33%
$\frac{1}{7}$	14.29%	$\frac{1}{16}$	6.25%

Multiply up for other numerators:

\frac{5}{16} = 31.25\%

\frac{5}{32} = 15.625\%

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 25 Sep 2024, Shift 3 · Q65Moderate

Example 2 · Data Interpretation · One Value as a Percentage of Another

Study the given bar-graph and answer the question that follows. The bar-graph shows the sales of books (in thousands) from six branches (B1, B2, B3, B4, B5 and B6) of a publishing company during two consecutive years 2000 and 2001. What percentage of the average sales of branches B1, B2 and B3 in 2001 is the average sales of branches B1, B3 and B6 in 2000?

Mixing up one-sixth and one-seventh

\frac{1}{6}

is 16.67% and

\frac{1}{7}

is 14.29%. Options are often built from the neighbouring fraction, so reduce fully before you read the table.

Drill 3 more on fractions and their percentage values

Concept 3 of 4: A part as a percentage of the whole

When the base is "the total", it is usually not printed: add up all the parts first. And when the table gives one group, the other group is what is left, so its percentage is 100% minus the first.

Definition

Share of the whole $= \frac{\text{part}}{\text{sum of all parts}} \times 100$ . Add every part the question includes in the whole.
The rest: if 48% passed, 52% did not. Either subtract the counts first or take 100% minus the given share.
Comparing rates across rows (qualified out of appeared, year by year): work out part $\div$ whole for each row. A bigger part does not mean a bigger rate when the wholes differ.

Share of the whole

\text{Share} = \frac{\text{part}}{\text{whole}} \times 100\% \qquad \%\,\text{rest} = 100\% - \%\,\text{share}

Worked example

The table shows a country's exports (in ₹ crore).

Item	Tea	Coffee	Spices	Rice
Exports	340	260	480	520

What percentage of the total exports is spices?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 26 Sep 2024, Shift 3 · Q69Easy

Example 3 · Data Interpretation · One Value as a Percentage of Another

The number of applicants appeared and qualified in a 4-wheeler driving licence test during the last four months of 2022 from a city are listed in the following table. Study the table carefully and answer the question that follows.

Month	Appeared applicants	Qualified applicants
September	2500	1200
October	2000	1100
November	2100	900
December	3000	1500

What is the percentage of disqualified applicants for the driving licence test in September?

Comparing parts instead of rates

A state with 920 qualified out of 9,200 in one year (10%) and 850 out of 7,000 in another (about 12.1%) did better in the second year, though fewer qualified. Compare part over whole for each row, never the parts alone.

Drill 7 more on a part as a percentage of the whole

Concept 4 of 4: Aggregate percentage of marks

A student's overall percentage is all the marks scored over all the marks possible. When every paper is out of 100, that is the plain average of the percentages. When papers carry different maximum marks, a bigger paper counts for more, so turn each percentage back into marks first.

Definition

Aggregate % $= \frac{\text{total marks obtained}}{\text{total maximum marks}} \times 100$ .
Table of percentages with different maximums: marks in a paper $= \frac{p}{100} \times$ its maximum. Add the marks, add the maximums, divide.
Equal maximums: the aggregate is the average of the percentages, and the total of marks out of $5 \times 100$ can be read off directly.
Best subject by percentage: compare marks $\div$ maximum for each subject, not the raw marks.
A pass mark in marks becomes a percentage of that paper's maximum (105 out of 175 is 60%).

Aggregate percentage

\text{Aggregate} = \frac{\sum \frac{p_i}{100} M_i}{\sum M_i} \times 100\%

p_ipercentage scored in paper i
M_imaximum marks of paper i

Worked example

The table shows a student's percentage in three papers, with the maximum marks in brackets.

Paper	English (100)	Science (150)	Maths (50)
Percentage	72	60	80

What is the student's aggregate percentage?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 19 Sep 2024, Shift 1 · Q73Easy

Example 4 · Data Interpretation · One Value as a Percentage of Another

The table given below shows the marks obtained by four students in 4 different subjects. Maximum marks for each subject is 175.

Student	Mathematics	Physics	Chemistry	English
Amit	105	98	109	86
Gunja	112	119	99	97
Arpit	103	121	94	100
Kavya	108	102	104	120

What is the aggregate percentage of marks obtained by Gunja in all the four subjects?

Averaging percentages from papers of different sizes

70% in a 150-mark paper is worth more marks than 70% in a 50-mark paper. When the maximums differ, convert each percentage to marks before adding.

Judging the best subject by raw marks

The subject with the most marks may also have the largest maximum. "Highest percentage" means marks divided by maximum for each subject.

Drill 7 more on aggregate percentage of marks

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)

One value as a percentage of another
A as a percentage of B
$\frac{A}{B} \times 100\%$
A part as a percentage of the whole
Share of the whole
$\text{Share} = \frac{\text{part}}{\text{whole}} \times 100\% \qquad \%\,\text{rest} = 100\% - \%\,\text{share}$
Aggregate percentage of marks
Aggregate percentage
$\text{Aggregate} = \frac{\sum \frac{p_i}{100} M_i}{\sum M_i} \times 100\%$

Reference tables (1)

Fractions and their percentage values8 rows

Fraction	Percentage	Fraction	Percentage
$\frac{1}{2}$	50%	$\frac{1}{8}$	12.5%
$\frac{1}{3}$	33.33%	$\frac{3}{8}$	37.5%
$\frac{2}{3}$	66.67%	$\frac{5}{8}$	62.5%
$\frac{1}{4}$	25%	$\frac{7}{8}$	87.5%
$\frac{3}{4}$	75%	$\frac{1}{9}$	11.11%
$\frac{1}{5}$	20%	$\frac{1}{11}$	9.09%
$\frac{1}{6}$	16.67%	$\frac{1}{12}$	8.33%
$\frac{1}{7}$	14.29%	$\frac{1}{16}$	6.25%

Multiply up for other numerators:

\frac{5}{16} = 31.25\%

\frac{5}{32} = 15.625\%

Watch out for (5)

Dividing by the wrong base
→ One value as a percentage of another
Mixing up one-sixth and one-seventh
→ Fractions and their percentage values
Comparing parts instead of rates
→ A part as a percentage of the whole
Averaging percentages from papers of different sizes
→ Aggregate percentage of marks
Judging the best subject by raw marks
→ Aggregate percentage of marks

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