Pie Chart DI — Degree-to-Percentage Speed Conversion

Pie chart DI is a staple of banking exams. The entire chart represents 360° or 100%, and each sector's angle determines its share. The key skill is converting between degrees, percentages, and actual values — fast.

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Core Formulas

Conversion	Formula
Degrees to Percentage	Percentage = (Degrees / 360) x 100
Percentage to Degrees	Degrees = (Percentage / 100) x 360
Degrees to Value	Value = (Degrees / 360) x Total
Percentage to Value	Value = (Percentage / 100) x Total

Simplified:

• 1° = 100/360 = 5/18 %
• 1% = 360/100 = 3.6°

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Benchmark Angle Table

Memorize this table. It eliminates the need for calculation on 80% of pie chart conversions.

Degrees	Percentage	Fraction of Total	Quick Mental Note
36°	10%	1/10	Base unit — everything builds from this
72°	20%	1/5	2 x 36°
90°	25%	1/4	Quarter circle
108°	30%	3/10	3 x 36°
120°	33.33%	1/3	One-third of circle
144°	40%	2/5	4 x 36°
180°	50%	1/2	Half circle
216°	60%	3/5	6 x 36°
240°	66.66%	2/3	Two-thirds of circle
270°	75%	3/4	Three-quarter circle
324°	90%	9/10	9 x 36°

Key Insight: Since 36° = 10% and 3.6° = 1%, you can handle ANY angle by splitting it into a benchmark plus a small remainder measured in multiples of 3.6°.

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Shortcut for Non-Standard Angles

For angles that are not exact benchmarks, split into nearest benchmark + remainder:

Rule: Every 3.6° = 1%. So the remainder in degrees / 3.6 = additional percentage.

Worked Conversions

93.6°:

• 90° = 25%
• Remainder: 93.6 - 90 = 3.6° = 1%
• Total: 25% + 1% = 26%

129.6°:

• 3.6 x 36 = 129.6°
• So 129.6° = 36%
• Or: 108° (30%) + 21.6° (6%) = 36%

104.4°:

• 108° = 30%
• Remainder: 108 - 104.4 = 3.6° = 1% (but we went below 108°, so subtract)
• Total: 30% - 1% = 29%

79.2°:

• 72° = 20%
• Remainder: 79.2 - 72 = 7.2° = 2%
• Total: 20% + 2% = 22%

64.8°:

• 72° = 20%
• Remainder: 72 - 64.8 = 7.2° = 2% (below 72°, so subtract)
• Total: 20% - 2% = 18%

Exam Tip: In the exam, you should NEVER do long division to convert degrees to percentages. The benchmark + remainder method gives you the answer in under 5 seconds.

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Pie Chart + Table Combined DI

This is the most common pie chart format in Mains-level exams. The pie chart gives the distribution of one quantity, and a table gives ratios or percentages to derive related quantities.

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Worked Example: Mustard Oil and Refined Oil

Pie Chart: Distribution of 1200 litres of mustard oil among sellers A-E.

Seller	Angle
A	72°
B	36°
C	90°
D	54°
E	108°

Verification: 72 + 36 + 90 + 54 + 108 = 360° (correct)

Table: Ratio of Mustard oil to Refined oil for each seller.

Seller	Mustard : Refined
A	2 : 1
B	2 : 3
C	3 : 1
D	6 : 5
E	36 : 25

Step 1: Convert Degrees to Mustard Oil Quantities

Use the formula: Mustard Oil = (Angle / 360) x 1200

Seller	Angle	Percentage	Mustard Oil (litres)
A	72°	20%	1200 x 20/100 = 240
B	36°	10%	1200 x 10/100 = 120
C	90°	25%	1200 x 25/100 = 300
D	54°	15%	1200 x 15/100 = 180
E	108°	30%	1200 x 30/100 = 360

Verification: 240 + 120 + 300 + 180 + 360 = 1200 (correct)

Step 2: Use Ratios to Find Refined Oil

The ratio Mustard : Refined tells us how to find Refined oil from the known Mustard oil.

If Mustard : Refined = a : b, then Refined = Mustard x (b/a)

Seller	Mustard	Ratio M:R	Refined Oil	Total Oil
A	240	2:1	240 x 1/2 = 120	360
B	120	2:3	120 x 3/2 = 180	300
C	300	3:1	300 x 1/3 = 100	400
D	180	6:5	180 x 5/6 = 150	330
E	360	36:25	360 x 25/36 = 250	610

Complete Data Table

Seller	Mustard Oil	Refined Oil	Total Oil
A	240	120	360
B	120	180	300
C	300	100	400
D	180	150	330
E	360	250	610

Total Refined Oil: 120 + 180 + 100 + 150 + 250 = 800 litres Total Oil (all types): 360 + 300 + 400 + 330 + 610 = 2000 litres

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Worked Question: External Variable with Pie Chart

Question: Mustard oil sold by A and B together = 18% of total oil sold by seller P. If P's ratio of mustard oil to refined oil is 3:2, find the difference between mustard oil sold by P and mustard oil sold by A.

Step-by-step:

Step 1: Find mustard oil by A and B together.

• A's mustard = 240, B's mustard = 120
• Total = 240 + 120 = 360 litres

Step 2: Find total oil sold by P.

• 360 = 18% of P's total oil
• P's total = 360 / 0.18

Shortcut: 18% = 18/100 = 9/50. So P's total = 360 x 50/9 = 40 x 50 = 2000 litres

Step 3: Find mustard oil sold by P.

• P's mustard : refined = 3 : 2
• P's mustard = 2000 x 3/5 = 1200 litres

Step 4: Find the difference.

• Difference = 1200 - 240 = 960

Answer: 960

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Speed Techniques for Pie Chart DI

Technique 1: Use Fractions, Not Decimals

When finding a sector's value:

• 72° out of 1200 = 1/5 of 1200 = 240 (instant)
• Do NOT compute 72/360 = 0.2, then 0.2 x 1200 = 240 (slower)

Technique 2: Check if Angles are Multiples of 36°

If all angles are multiples of 36°, every sector is a clean percentage (multiple of 10%). This makes all calculations clean.

If angles are multiples of 3.6°, every sector is a whole percentage. Still clean.

If angles have decimals that are NOT multiples of 3.6°, expect messy calculations — approximate if options are far apart.

Technique 3: Ratio Simplification Before Multiplication

For Seller E: Mustard = 360, Ratio = 36:25.

• Refined = 360 x 25/36
• Simplify first: 360/36 = 10, so Refined = 10 x 25 = 250

Always cancel common factors before multiplying.

Technique 4: Verify with Total

After computing all values in a column, add them up. If they don't match the expected total, you have an error somewhere. This 10-second check prevents wrong answers on 3-4 subsequent questions.

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Common Pie Chart Question Types

Type	Approach
"What fraction of total oil is refined oil by C?"	Refined C / Grand Total = 100/2000 = 1/20
"Mustard by D is what % more than refined by C?"	((180-100)/100) x 100 = 80%
"Find the average refined oil across all sellers"	800/5 = 160
"Ratio of total oil of A to total oil of B?"	360:300 = 6:5
"If E's mustard increases by 20%, new mustard?"	360 x 6/5 = 432

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Summary

1. 360° = 100% and 3.6° = 1% — these two facts solve every conversion.
2. Memorize the benchmark angle table (36°=10%, 72°=20%, 90°=25%, 108°=30%, 180°=50%).
3. For non-standard angles, use benchmark + remainder (every 3.6° extra = 1% more).
4. In Pie + Table combined DI, first convert angles to values, then use the table's ratios to derive the second variable.
5. Cancel common factors before multiplying ratios — this is where most time is saved.
6. Verify your column totals after building the table — one wrong cell leads to 3-4 wrong answers.

Summary Cheat Sheet

Concept / Topic	Key Details / Explanation
Core formula	360° = 100%. 3.6° = 1%. 1° = 5/18 %
Degrees → Value	Value = (Degrees / 360) × Total. Shortcut: convert to % first, then multiply
36° = 10%	Base benchmark — every other angle is a multiple of 36°
72° = 20%	2 × 36° = 1/5 of total
90° = 25%	Quarter circle = 1/4
108° = 30%	3 × 36° = 3/10
120° = 33.33%	One-third of circle = 1/3
144° = 40%	4 × 36° = 2/5
180° = 50%	Half circle = 1/2
216° = 60%	6 × 36° = 3/5
270° = 75%	Three-quarter circle = 3/4
Non-standard angle shortcut	Split into nearest benchmark + remainder. Each 3.6° remainder = 1%. E.g., 93.6° = 90° + 3.6° = 25% + 1% = 26%
Pie + Table: Refined from Ratio	If Mustard : Refined = a : b, then Refined = Mustard × (b/a)
Cancel before multiplying	Always simplify fractions before computing. E.g., 360 × 25/36 = 10 × 25 = 250
Verify column sums	Individual values must add up to pie chart total. Do this check before answering any question
18% shortcut	18% = 9/50, so ÷ 18% = × 50/9
Common mistake: not using fractions	72° of 1200 = 1/5 × 1200 = 240 (instant). Do NOT compute 72/360 = 0.2 then × 1200 (slower)
External variable pattern	A+B = k% of P's total → P's total = (A+B) / (k/100). Then apply ratio to split P's total