SSC CGL Maths · Data Interpretation

Two-Step Share Problems

A two-step question first finds a group as a share of a total, then splits that group again by a ratio or a second percentage, or runs the same chain backwards from a known part.

All Data Interpretation notes

Why this matters

Seventeen questions in the bank, and twelve of them are MODERATE: this is where the chapter's harder marks sit. Each step is one you have met on the earlier pages; the work is keeping the chain in order and multiplying the fractions together before touching the big total.

Concept 1 of 2: A ratio or a percentage inside a share

The table gives a share of a population (below the poverty line, opted for Biology, in department D) and then splits that share again (men to women, boys to girls, 30% female). Find the group, then split it. Better still, multiply the two fractions first and apply them to the total once.

Definition

Step 1: group $=$ share $\times$ total (or number of zones $\times$ average per zone).
Step 2, a ratio $a : b$ : the $b$ part $= \frac{b}{a + b} \times$ group. Step 2, a percentage $q\%$ : $\frac{q}{100} \times$ group.
Fast route: multiply the fractions first. 30% then $\frac{2}{3}$ is $\frac{3}{10} \times \frac{2}{3} = \frac{1}{5}$ of the total. 60% of a 25% share is 15% of the whole.
Two groups together: split each group on its own, add the parts, and only then form the ratio. Ratios from different groups are never added.
The remaining part comes from the other side of the ratio, or from 100% minus the given percentage.

A part inside a share

\text{Part} = \text{Total} \times \frac{p}{100} \times \frac{b}{a + b}

pthe group's percentage of the total
a : bthe ratio that splits the group; b is the wanted side

Worked example

A town of 12,000 people has 35% graduates, and the graduates are men and women in the ratio

4 : 3

. How many women graduates are there?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 25 Jul 2023, Shift 3 · Q75Easy

Example 1 · Data Interpretation · Two-Step Share Problems

The following table shows the percentage of population of four states below poverty line and the proportion of males and females below and above poverty line.

State	Percentage of Population Below Poverty Line	Below Poverty Line (Males : Females)	Above Poverty Line (Males : Females)
A	10%	2 : 3	4 : 5
B	25%	3 : 5	3 : 2
C	28%	1 : 4	5 : 3
D	38%	7 : 1	7 : 4

If the total population of State B is 7,200, then what is the number of females below poverty line in that state?

Adding ratios from different groups

5 : 7

in one school and

2 : 3

in another do not combine to

7 : 10

. Work out the boys and girls in each school, add the counts, then form the ratio.

Applying the second percentage to the whole total

"30% of the employees in department D are women" means 30% of department D, not 30% of the company. Find the department first.

Drill 10 more on a ratio or a percentage inside a share

Concept 2 of 2: Working back to a missing total

Here the chain is the same, but the question hands you the end of it (the number of women who qualified, the literate men, the marked price) and asks for the start. Undo each step in reverse order: a ratio part back to the group, the group back to the total.

Definition

From a ratio part to the group: if the women are 5 parts of 8 and number 150, one part is 30 and the group is $8 \times 30 = 240$ .
From a percentage back to the total: total $=$ group $\div \frac{p}{100}$ .
Both at once: total $=$ known part $\div$ (product of the fractions).
A missing entry in a table: subtract the known entries from the printed total first. "B is 20% less than M" means $B = 0.8M$ , so $B + M = 1.8M$ .
A price above cost: if the marked price is $r\%$ above cost, cost $=$ marked price $\div (1 + \frac{r}{100})$ .

Back to the total

\text{Total} = \frac{\text{known part}}{\frac{p}{100} \times \frac{b}{a + b}}

Worked example

Of the candidates who appeared in a test, 45% qualified. Among those who qualified, men and women were in the ratio

4 : 5

. If 270 women qualified, how many candidates appeared?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 11 Sep 2024, Shift 1 · Q69Moderate

Example 2 · Data Interpretation · Two-Step Share Problems

Study the given table and answer the question that follows. The given table shows the number of candidates who appeared (both male and female) in a Public Examination and the percentage of those who qualified in the examination from two states X and Z. Few values are missing in the table (indicated by ------). You will be required to fill them up according to the question.

Year	State X: Number of appeared candidates	State X: Percentage of qualified candidates	State Z: Number of appeared candidates	State Z: Percentage of qualified candidates
2008	480	$70\%$	------	$70\%$
2009	560	$75\%$	500	$80\%$
2010	--------	$60\%$	650	$50\%$
2011	450	$89\%$	720	$72\%$
2012	790	------	660	------

Out of the number of qualified candidates from State X in 2010, the ratio of male to female candidates is

5 : 7

. If the number of female qualified candidates from State X in 2010 is 168, what is the number of appeared candidates (both male and female) from State X in 2010?

Undoing only one step of the chain

If 270 women are

\frac{5}{9}

of those who qualified, 486 is the number who qualified, not who appeared. Divide by the qualifying rate as well.

Reading 20% less as 20% of

"B is 20% less than M" makes B equal to 80% of M. Writing B as 20% of M, or M as 120% of B, gives a wrong pair.

Drill 5 more on working back to a missing total

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 (2)

A ratio or a percentage inside a share
A part inside a share
$\text{Part} = \text{Total} \times \frac{p}{100} \times \frac{b}{a + b}$
Working back to a missing total
Back to the total
$\text{Total} = \frac{\text{known part}}{\frac{p}{100} \times \frac{b}{a + b}}$

Watch out for (4)

Adding ratios from different groups
→ A ratio or a percentage inside a share
Applying the second percentage to the whole total
→ A ratio or a percentage inside a share
Undoing only one step of the chain
→ Working back to a missing total
Reading 20% less as 20% of
→ Working back to a missing total

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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