Calculating percentage from degrees in a pie chart
Question
A pie chart gives the expenditure on five different items A, B, C, D and E in a household. If B, C, D and E correspond to 90°, 50°, 45° and 75° respectively, then what is the percentage of expenditure on item A?
Options
112/9
125/6
155/9
250/9
Explanation
A complete pie chart represents 100\% of the data and spans a full geometric circle of 360^\circ. Calculate the sum of the provided sector angles: Sum (B, C, D, E) = 90^\circ + 50^\circ + 45^\circ + 75^\circ = 260^\circ.
The remaining angle for sector A is: Angle A = 360^\circ - 260^\circ = 100^\circ.
Convert this angular footprint into a percentage of the whole pie: Percentage = \left( 100/360 \right) × 100\% Simplify the fraction: 10/36 × 100\% = 1000/36\%. Divide the numerator and denominator by 4: 250/9\%.
Answer: (d).
Question details
Year
2022
Paper
CSAT
Question
Q70
Section
Data Interpretation & Sufficiency
Sub-topic
Data Interpretation (Pie Chart)
Type
Factual single
Difficulty
Easy
Source hint
Pie chart expenditure A, B, C, D, E
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