The table shows the monthly expenditure on different items:
| Item | Food | Clothing | Rent | Education | Misc. |
|---|---|---|---|---|---|
| Expenditure (in Rs.) | 4000 | 2000 | 1500 | 1500 | 1000 |
What is the difference between the central angles of the sectors for Food and Rent when the data given in the table is presented in a pie chart?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 90°
In a pie chart the whole circle, 360°, is shared in proportion to the values, so central angle = (value ÷ total) × 360°.
Total monthly expenditure \(=4000+2000+1500+1500+1000=10000\)
Central angle for Food: \(\displaystyle \frac{4000}{10000}\times360^\circ=144^\circ\)
Central angle for Rent: \(\displaystyle \frac{1500}{10000}\times360^\circ=54^\circ\)
Difference between the two angles \(=144^\circ-54^\circ=90^\circ\)
Shortcut: The difference of two angles is the angle of the difference of the two values.
Food − Rent \(=4000-1500=2500\), a quarter of the total 10000
A quarter of 360° is 90°