SSC CGL Maths · Data Interpretation

Pie Charts and Shares of a Total

A pie chart, or a table of percentage shares, splits one total into parts; each part is its share times the total, and 100% of the total is the full 360° of the circle.

All Data Interpretation notes

Why this matters

Forty-eight questions in the bank, the biggest page of the chapter, and forty-three of them are EASY. Most are a single multiplication, so the time goes on spotting the shortcut: add the shares before multiplying, use 1% of the total, or compare sectors without the total at all.

Concept 1 of 4: From a percentage share to a value

If a sector is 25% of a ₹80,000 budget, it is a quarter of ₹80,000. When a question asks about two sectors together, or the gap between two sectors, work with their percentages first and multiply by the total only once.

Definition

Value $= \frac{p}{100} \times$ total.
Two or more sectors: add their percentages first (13% and 17% make 30%), then multiply once.
Difference of two sectors: subtract the percentages first (40% minus 8% is 32%), then multiply once.
Fast route: find 1% of the total (₹54,000 gives ₹540) and multiply by the share; 10% and 5% are just as quick.
A table of percentages with a different total for each year: each year's percentage applies to that year's total only. Turn both into numbers before you compare.
If the question says to neglect the decimal part, round down only at the very end.

Value of a share

\text{Value} = \frac{p}{100} \times \text{Total}

pthe sector's percentage

Worked example

A family's monthly spending of ₹60,000 is split as shown.

Head	Rent	Food	Travel	Savings	Others
Share	30%	25%	12%	18%	15%

How much does the family spend on Rent and Travel together?

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 · Q52Easy

Example 1 · Data Interpretation · Pie Charts and Shares of a Total

The following pie-chart shows the distribution of students at graduate level in different institutes in a town. Study the given chart and answer the question that follows. Distribution of students at graduate level institutes If the total number of students at the graduate level is 2,46,000, then how many students of institutes A and B are studying at graduate level?

Comparing percentages across different totals

22% of 18,000 is more than 24% of 15,000. When each year has its own total, a smaller share can still be a bigger number, so convert to numbers before comparing.

Rounding each share before adding

Add the percentages, multiply once, and round only at the end. Rounding each sector's value first can land one unit away, on a neighbouring option.

Drill 22 more on from a percentage share to a value

Concept 2 of 4: Degrees and central angles in a pie chart

The whole circle is 360° and stands for 100% of the total, so every 1% is 3.6°. Some charts print degrees instead of percentages; a sector's share is then its angle over 360.

Definition

Angle from a percentage: $\theta = p \times 3.6^\circ$ . 25% is 90°, 10% is 36°, 50% is 180°.
Value from an angle: value $= \frac{\theta}{360^\circ} \times$ total.
Percentage from an angle: $\frac{\theta}{360} \times 100$ , or $\theta \div 3.6$ .
Angle from raw values: add all the values for the total, then $\theta = \frac{\text{value}}{\text{total}} \times 360^\circ$ .
Check: the angles of a chart add to 360°, and the percentages to 100%. If a total is given in the question but you are asked only for an angle, the total is not needed.

Pie chart angles

\text{Value} = \frac{\theta}{360^\circ} \times \text{Total} \qquad \theta = \frac{p}{100} \times 360^\circ = 3.6p^\circ

$\theta$ the sector's central angle
pthe sector's percentage

Worked example

In a pie chart of 2,000 students, the sector for Commerce has a central angle of 54°. What percentage of the students study Commerce, and how many is that?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 24 Jul 2023, Shift 4 · Q58Easy

Example 2 · Data Interpretation · Pie Charts and Shares of a Total

The given chart shows the marks scored by a class X student in different subjects. If the total marks are 1800, then find the marks in social science.

Reading degrees as percentages

A sector marked 45° is 12.5% of the total, not 45%. Check the chart's heading: "values are in degrees" means divide by 360, not 100.

Using 100 where 360 belongs

An angle is a share of 360°. A 15% sector is

15 \times 3.6 = 54^\circ

, not

15^\circ

Drill 14 more on degrees and central angles in a pie chart

Concept 3 of 4: From one known share to the total or another share

Sometimes the total is hidden and one sector's value is given instead. If 24% is ₹21,600, then 1% is ₹900, and every other sector, or the whole, follows by multiplying.

Definition

1% of the total $= \frac{V}{p}$ , where the known sector is $p\%$ and has value $V$ .
Total $= 100 \times \frac{V}{p}$ .
Another sector of $q\%$ $= V \times \frac{q}{p}$ ; there is no need to find the total first.
Several known sectors together: add their percentages first, then divide.
The same works in degrees: if a 40° sector stands for 600, each degree stands for 15.

From a known share

\text{Total} = \frac{V}{p} \times 100 \qquad \text{Other share} = V \times \frac{q}{p}

Vthe known sector's value
pthe known sector's percentage
qthe wanted sector's percentage

Worked example

In a pie chart of a family's income, Housing is 24% and comes to ₹21,600. Food is 18%. Find the total income and the amount spent on Food.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2024 · Tier I, 12 Sep 2024, Shift 2 · Q73Easy

Example 3 · Data Interpretation · Pie Charts and Shares of a Total

The following pie chart shows the study time of different subjects of a student in a day. Study the pie chart and answer the question. If the student studied English for 3 hours, then he studied Mathematics for:

Dividing by the wanted share instead of the known one

1% of the total comes from the sector whose value you know. If 24% is ₹21,600, divide by 24, not by the 18% you are asked about.

Drill 5 more on from one known share to the total or another share

Concept 4 of 4: Comparing sectors without working out the total

Every sector of one chart is the same total multiplied by its own share. So when two sectors of one chart are compared (a ratio, a percentage, how many times), the total cancels and the percentages or the degrees answer the question by themselves.

Definition

Within one chart: sector A : sector B $=$ $p_A : p_B$ $=$ $\theta_A : \theta_B$ .
A as a percentage of B, or A more or less than B by a percentage, works the same way on the shares.
A total printed in the question is often a decoy here: it cancels, so do not compute amounts.
Two charts drawn on the same total (the sources and the uses of one ₹10 lakh fund): the total still cancels, so their percentages compare directly.
Two charts with different totals (1,800 appeared and 800 passed, or two years): the total does not cancel. Turn each sector into a number first.

Comparing sectors of one chart

\frac{\text{Sector } A}{\text{Sector } B} = \frac{p_A}{p_B} = \frac{\theta_A}{\theta_B}

Worked example

In a pie chart of a company's spending, Transport has a 75° sector and Food a 120° sector. Transport spending is what percentage of Food spending, and by what percent is it less?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2023 · Tier I, 17 Jul 2023, Shift 4 · Q52Easy

Example 4 · Data Interpretation · Pie Charts and Shares of a Total

Study the given pie-chart carefully and answer the following question. If scholarship has to be paid out of the donation fund, then what is the percentage of donation fund used for this purpose (rounded off to two decimal places)?

Comparing sectors of charts with different totals directly

A 25% sector of the passed students and a 100° sector of the appeared students cannot be compared as shares, because the two charts stand for different totals. Convert each to a number of students first; only charts on the same total compare share to share.

Drill 3 more on comparing sectors without working out the 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 (4)

From a percentage share to a value
Value of a share
$\text{Value} = \frac{p}{100} \times \text{Total}$
Degrees and central angles in a pie chart
Pie chart angles
$\text{Value} = \frac{\theta}{360^\circ} \times \text{Total} \qquad \theta = \frac{p}{100} \times 360^\circ = 3.6p^\circ$
From one known share to the total or another share
From a known share
$\text{Total} = \frac{V}{p} \times 100 \qquad \text{Other share} = V \times \frac{q}{p}$
Comparing sectors without working out the total
Comparing sectors of one chart
$\frac{\text{Sector } A}{\text{Sector } B} = \frac{p_A}{p_B} = \frac{\theta_A}{\theta_B}$

Watch out for (6)

Comparing percentages across different totals
→ From a percentage share to a value
Rounding each share before adding
→ From a percentage share to a value
Reading degrees as percentages
→ Degrees and central angles in a pie chart
Using 100 where 360 belongs
→ Degrees and central angles in a pie chart
Dividing by the wanted share instead of the known one
→ From one known share to the total or another share
Comparing sectors of charts with different totals directly
→ Comparing sectors without working out the total

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