SSC CGL Maths · Data Interpretation

Ratios from Data

A ratio from a table compares two totals in the order the question names them, cut down to lowest terms.

Why this matters

Thirty questions in the bank, twenty-seven of them EASY and three from 2025. The adding is quick; marks are lost by writing the ratio the wrong way round or stopping before lowest terms, and the options are built to catch both.

Concept 1 of 3: Ratio of two totals in lowest terms

Add up each side the question names, write first total : second total, and divide both by their highest common factor. With four options on screen you can often skip the full simplifying: the right option, scaled up, gives back both totals.

Definition

Order: "the ratio of A to B" is A : B. "Respective ratio" also follows the order the items are named.
Full method: add each side, then divide both totals by their HCF.
Fast route: divide in steps by easy factors (10, 5, 2, 3) until nothing common is left, or test the options: if $a : b$ is right, then $\frac{\text{total}_1}{a} = \frac{\text{total}_2}{b}$ .
A ratio of two values from the same chart can be taken straight from the readings; their common unit cancels.

Ratio in lowest terms

a : b = \frac{a}{h} : \frac{b}{h}, \quad h = \text{HCF}(a, b)

Worked example

The table shows the number of students in two subjects in four colleges.

Subject	W	X	Y	Z
Physics	210	185	240	215
Chemistry	160	165	200	175

What is the ratio of the total number of Physics students to the total number of Chemistry students?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 25 Sep 2024, Shift 2 · Q63Easy

Example 1 · Data Interpretation · Ratios from Data

The given table shows the number of clerical and officer cadre employees recruited by four different banks A, B, C and D from 2011 to 2014.

Year	A Officer	A Clerk	B Officer	B Clerk	C Officer	C Clerk	D Officer	D Clerk
2011	260	458	255	460	205	428	265	470
2012	310	569	286	584	230	539	246	554
2013	350	730	321	725	340	740	361	725
2014	400	890	452	845	380	850	482	860

Compute the ratio of the number of officer cadre employees of bank A to the number of officer cadre employees of bank C.

Writing the ratio the wrong way round

"The ratio of A to B" puts A first. Both orders nearly always appear among the options, so the order decides the mark.

Stopping before lowest terms

180 : 225

and

4 : 5

are the same ratio, but the options print only the reduced form. Keep dividing until the two numbers share no factor.

Drill 20 more on ratio of two totals in lowest terms

Concept 2 of 3: How many times, and ratios of averages

"How many times" is one value divided by the other. A ratio of two averages looks like extra work, but if both averages are over the same number of entries the divisions cancel, and the ratio of the averages is the ratio of the totals.

Definition

"A is how many times B" $= A \div B$ . It is a single number such as 1.8, not a ratio.
Ratio of two averages over the same count $=$ ratio of the two totals.
Ratio of one value to an average: work out the average first, then write value : average and simplify.
Over different counts, divide each total by its own count before comparing.

Ratio of averages over the same count

\frac{\bar{x}}{\bar{y}} = \frac{\sum x_i \div n}{\sum y_i \div n} = \frac{\sum x_i}{\sum y_i}

Worked example

A country imported 2,250 tonnes of a crop in 2019 and 4,050 tonnes in 2021. The 2021 imports were how many times the 2019 imports?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 21 Jul 2023, Shift 3 · Q59Easy

Example 2 · Data Interpretation · Ratios from Data

Study the given table and answer the question that follows. The table gives the number of graduate students enrolled in 4 different colleges A, B, C, and D in a city over the years 2010 to 2014 and also the number of students who passed in the final examination during these years.

Year	2010	2010	2011	2011	2012	2012	2013	2013	2014	2014
College	Enrolled	Pass	Enrolled	Pass	Enrolled	Pass	Enrolled	Pass	Enrolled	Pass
A	680	620	600	560	720	700	800	760	750	700
B	550	530	450	420	600	550	650	620	700	680
C	480	450	520	500	580	550	620	600	720	700
D	710	650	750	710	680	640	720	690	740	710

Find the ratio of the average of students enrolled from college D to the average of students who passed from college D over all the years.

Dividing averages that cover different counts

The ratio of averages equals the ratio of totals only when both are over the same number of entries. A 3-year average against a 5-year average needs each division done.

Drill 3 more on how many times, and ratios of averages

Concept 3 of 3: Finding each part before taking the ratio

Sometimes the table does not print the two numbers the ratio needs. It prints a total and one part, or overlapping groups, or a ratio that links two columns. Build the two parts first; the ratio is then the easy last line.

Definition

Total and one part given: the other part $=$ total $-$ the given part (men $=$ all scholars $-$ women).
Overlapping groups: everyone who plays football $=$ "football and basketball" $+$ "football only". The "neither" row belongs to no group.
A given ratio links two values: if exports : imports $= p : q$ , then imports $=$ exports $\times \frac{q}{p}$ .
Part to total: add the whole column first, then write part : total.

Recovering a value from a ratio

E : I = p : q \;\Rightarrow\; I = E \times \frac{q}{p}

Ethe value you know
Ithe value you want

Worked example

A club of 150 members is surveyed.

Category	Members
Play chess and carrom	40
Play chess but not carrom	55
Play carrom but not chess	30
Play neither	25

What is the ratio of chess players to carrom players?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 13 Sep 2025, Shift 2 · Q54Easy

Example 3 · Data Interpretation · Ratios from Data

Determine the ratio of the number of students who play Football to the number of students who play Basketball in a survey of 120 students from the following table:

Category	Number
Play Football and Basketball	25
Play Football but not Basketball	45
Play Basketball but not Football	35
Play neither sport	15

Counting only the "only" row

Everyone who plays football includes those who play football and basketball. The row "football but not basketball" is only part of the football players.

Drill 4 more on finding each part before taking the ratio

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)

Ratio of two totals in lowest terms
Ratio in lowest terms
$a : b = \frac{a}{h} : \frac{b}{h}, \quad h = \text{HCF}(a, b)$
How many times, and ratios of averages
Ratio of averages over the same count
$\frac{\bar{x}}{\bar{y}} = \frac{\sum x_i \div n}{\sum y_i \div n} = \frac{\sum x_i}{\sum y_i}$
Finding each part before taking the ratio
Recovering a value from a ratio
$E : I = p : q \;\Rightarrow\; I = E \times \frac{q}{p}$

Watch out for (4)

Writing the ratio the wrong way round
→ Ratio of two totals in lowest terms
Stopping before lowest terms
→ Ratio of two totals in lowest terms
Dividing averages that cover different counts
→ How many times, and ratios of averages
Counting only the "only" row
→ Finding each part before taking the ratio

Test yourself on Data Interpretation

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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