Pie Charts
Pie chart DI for CGPSC CSAT: converting degrees, percentages and amounts, and comparing two pie charts with different totals — with practice MCQs and speed drills.
Prerequisites
- Percentages — the fraction–percentage table makes degree conversions instant.
- Tables — the “share of total” question type, which is all a pie chart shows.
- Ratio and Proportion — ratios of sectors equal ratios of their angles.
The Hook: The Shrinking Slice That Grew
Every budget season, newspapers print the state budget as a pie chart (वृत्त चित्र): “Where each rupee goes”. Suppose the education slice looks thinner this year than last year — 22% instead of 25%. A reader concludes: “The government is spending less on schools.”
Not necessarily. If the whole budget grew from ₹600 crore to ₹750 crore (hypothetical figures), then 25% of 600 is ₹150 crore and 22% of 750 is ₹165 crore — education spending actually rose by 10%. A smaller slice of a bigger pie can be more.
The question this page answers: how do you move between degrees, percentages and amounts in a pie chart, and how do you compare two pies without falling for the slice-size illusion?
Why it matters for CGPSC: a pie chart is the standard way to show the composition of a whole — a budget, land use, a household’s spending, sources of revenue. CSAT pie questions are short and formula-driven, so they are quick marks once the conversions are automatic.
The Three Conversions
A full circle is 360° and stands for 100% of the total. So 1% = 3.6°.
$$\boxed{\text{Degrees} = \text{Percent}\times 3.6} \qquad \boxed{\text{Percent} = \frac{\text{Degrees}}{3.6}}$$$$\boxed{\text{Amount} = \frac{\text{Degrees}}{360}\times \text{Total} = \frac{\text{Percent}}{100}\times \text{Total}}$$Degree–percentage table (memorise)
| Degrees | Percent | Fraction | Degrees | Percent | Fraction |
|---|---|---|---|---|---|
| 18° | 5% | \( \frac{1}{20} \) | 90° | 25% | \( \frac{1}{4} \) |
| 36° | 10% | \( \frac{1}{10} \) | 108° | 30% | \( \frac{3}{10} \) |
| 45° | 12.5% | \( \frac{1}{8} \) | 120° | \( 33\frac{1}{3}\% \) | \( \frac{1}{3} \) |
| 54° | 15% | \( \frac{3}{20} \) | 144° | 40% | \( \frac{2}{5} \) |
| 60° | \( 16\frac{2}{3}\% \) | \( \frac{1}{6} \) | 180° | 50% | \( \frac{1}{2} \) |
| 72° | 20% | \( \frac{1}{5} \) | 270° | 75% | \( \frac{3}{4} \) |
Pie Chart 1: Given in Percentages
A hypothetical district’s annual plan outlay of ₹600 crore (Year 1) — practice figures, not official data
pie showData
title District plan outlay, Year 1 (percent, hypothetical)
"Education" : 25
"Agriculture" : 20
"Rural development" : 18
"Health" : 15
"Rural roads" : 12
"Others" : 10| Head | Percent | Central angle | Amount (₹ crore) |
|---|---|---|---|
| Education | 25% | 90° | 150 |
| Agriculture | 20% | 72° | 120 |
| Rural development | 18% | 64.8° | 108 |
| Health | 15% | 54° | 90 |
| Rural roads | 12% | 43.2° | 72 |
| Others | 10% | 36° | 60 |
| Total | 100% | 360° | 600 |
By what percent is the outlay on agriculture more than that on health?
Within one pie the total is common, so compare the percentages directly: \( \frac{20 - 15}{15}\times 100 = 33\frac{1}{3}\% \). No need to compute ₹120 crore and ₹90 crore.
Note: the difference “20% − 15% = 5” is in percentage points of the total — a different answer to a different question.
Pie Chart 2: Given in Degrees
A hypothetical family’s monthly spending; monthly income ₹48,000 — practice figures
| Item | Central angle | Percent | Amount (₹) |
|---|---|---|---|
| Food | 120° | \( 33\frac{1}{3}\% \) | 16,000 |
| Rent | 72° | 20% | 9,600 |
| Education | 54° | 15% | 7,200 |
| Savings | 45° | 12.5% | 6,000 |
| Transport | 36° | 10% | 4,800 |
| Others | 33° | about 9.2% | 4,400 |
| Total | 360° | 100% | 48,000 |
Spending on food is how much more than spending on rent, in rupees?
Difference in angle = \( 120° - 72° = 48° \). Amount = \( \frac{48}{360}\times 48000 = 6400 \). One step, no need to find each amount separately.
Comparing Two Pie Charts
When two pies have different totals, a share can fall while the amount rises. Always multiply by each pie’s own total.
Year 2 of the same hypothetical district: total outlay ₹750 crore
| Head | Year 1 share | Year 1 amount | Year 2 share | Year 2 amount | Change in amount |
|---|---|---|---|---|---|
| Education | 25% | 150 | 22% | 165 | +10% |
| Agriculture | 20% | 120 | 20% | 150 | +25% |
| Rural development | 18% | 108 | 20% | 150 | about +38.9% |
| Health | 15% | 90 | 16% | 120 | about +33.3% |
| Rural roads | 12% | 72 | 14% | 105 | about +45.8% |
| Others | 10% | 60 | 8% | 60 | 0% |
Shortcut: if a head’s share is unchanged, its amount changes by the same percentage as the total (here +25%). A head beats the total’s growth only if its share rose.
Memory Tricks
- “1% = 3.6°; 10% = 36°; 25% = 90°.” Build everything else from these three.
- “Degrees over 360, times the total.” One formula for every amount question.
- Same pie — compare angles; two pies — compare amounts. Inside one pie, ratios of angles are ratios of amounts. Across pies, multiply by each total first.
- “Share flat = grows with the total.”
Don’t Confuse
| This | vs | That |
|---|---|---|
| Share fell (25% → 22%) | Amount fell (not necessarily — here it rose 10%) | |
| Food − Rent = 48° = 13⅓ percentage points | Food is 66⅔% more than Rent | |
| Ratio of two sectors in one pie = ratio of angles | Ratio across two pies needs both totals | |
| Central angle (out of 360) | Percentage (out of 100) |
Common Mistakes
Practice
All figures are hypothetical and refer to the pie charts and tables above.
Level 1: Foundation
- What is the central angle for Education in Year 1?
- What is the Year 1 outlay on Health?
- A sector of 72° represents what percent of the total?
- How much does the family save each month?
Answers
- \( 25 \times 3.6 = \) 90°.
- 15% of ₹600 crore = ₹90 crore.
- \( \frac{72}{3.6} = \) 20%.
- \( \frac{45}{360}\times 48000 = \frac{1}{8}\times 48000 = \) ₹6,000.
Level 2: Prelims MCQs
Q1. In the Year 1 pie chart, the central angle of the sector for Rural roads is:
(a) 36° (b) 43.2° (c) 48° (d) 54°
Answer: (b) 43.2°
Q2. The family’s spending on food is what percent more than its spending on rent?
(a) 20% (b) 40% (c) 48% (d) \( 66\frac{2}{3}\% \)
Answer: (d) 66⅔%
Within one pie, compare angles: \( \frac{120 - 72}{72}\times 100 = \frac{48}{72}\times 100 = 66\frac{2}{3}\% \).
Option (c) is the degree difference (48°) wrongly read as a percentage; check with amounts: ₹16,000 vs ₹9,600, difference ₹6,400, and \( \frac{6400}{9600} = \frac{2}{3} \).
Q3. Comparing Year 1 (total ₹600 crore) with Year 2 (total ₹750 crore), consider the following statements:
- The share of Education in the total outlay fell.
- The amount spent on Education fell.
- The amount spent on Others remained unchanged.
Which of the statements given above is/are correct?
(a) 1 only (b) 1 and 2 only (c) 1 and 3 only (d) 2 and 3 only
Answer: (c) 1 and 3 only
Q4. Match the head (List I) with its central angle in the Year 1 pie chart (List II):
| List I (Head) | List II (Angle) |
|---|---|
| A. Health | 1. 36° |
| B. Agriculture | 2. 64.8° |
| C. Rural development | 3. 54° |
| D. Others | 4. 72° |
(a) A-3, B-4, C-2, D-1 (b) A-4, B-3, C-2, D-1 (c) A-3, B-2, C-4, D-1 (d) A-1, B-4, C-2, D-3
Answer: (a) A-3, B-4, C-2, D-1
Q5. Which head recorded the highest percentage increase in amount from Year 1 to Year 2?
(a) Health (b) Agriculture (c) Rural roads (d) Rural development
Answer: (c) Rural roads
Amounts (₹ crore): Health 90 → 120 (about +33.3%); Agriculture 120 → 150 (+25%); Rural roads 72 → 105 (about +45.8%); Rural development 108 → 150 (about +38.9%).
Shortcut: the amount grows by the total’s factor (\( 1.25 \)) times the share’s factor. Rural roads’ share grew most in relative terms (\( \frac{14}{12} \approx 1.17 \)), so its amount grew most.
Level 3: Speed Drill — Solve in 60 Seconds
- Convert 27° to a percentage.
- Convert 18% to degrees.
- In a pie chart of total ₹2,400, what amount does a 75° sector represent?
- The family’s combined spending on Education and Transport.
- If the family’s income rises to ₹60,000 and food still takes 120°, what is the food spend?
- Ratio of Health to Rural roads outlay in Year 2.
Answers with the shortcut used
- 7.5% — \( \frac{27}{3.6} \); or 18° = 5% and 9° = 2.5%.
- 64.8° — \( 18 \times 3.6 \); or 20% = 72° minus 2% = 7.2°.
- ₹500 — \( \frac{75}{360} = \frac{5}{24} \); \( \frac{2400}{24}\times 5 \).
- ₹12,000 — \( 54° + 36° = 90° = \frac{1}{4} \) of ₹48,000.
- ₹20,000 — 120° is one-third of the income.
- 8 : 7 — 16% : 14% of the same total, i.e. 120 : 105.
Quick Revision Table
| Idea | Formula / Fact |
|---|---|
| Full circle | 360° = 100%; 1% = 3.6° |
| Degrees → percent | Divide by 3.6 |
| Percent → degrees | Multiply by 3.6 |
| Degrees → amount | \( \frac{\text{Degrees}}{360}\times\text{Total} \) |
| Within one pie | Ratio of amounts = ratio of angles |
| Across two pies | Multiply each share by its own total |
| Share unchanged | Amount grows at the same rate as the total |
Key Takeaways
- 360° = 100%, so 1% = 3.6°. Know the common pairs (36° = 10%, 72° = 20%, 90° = 25%, 120° = \( 33\frac{1}{3}\% \)).
- For amounts, go straight from degrees: \( \frac{\text{Degrees}}{360}\times\text{Total} \).
- Inside one pie, compare angles or percentages directly — the total cancels.
- Across two pies with different totals, a falling share can hide a rising amount.
- A difference of degrees or percentages is in percentage points of the total, not a percent change.
What’s Next
- Data Sufficiency — the last topic of this chapter: is the data enough?
- Bar and Line Graphs — trends over time rather than shares of a whole.
- Tables — the share and growth question types in table form.
- Public Finance — budgets are the classic real-world pie chart; read the official “rupee comes from / rupee goes to” charts there.
- Data Interpretation — Quick Revision — the whole chapter on one page.