Discussion
The monthly expenditure of a family is represented in a pie chart. The central angle for Food is 108° and for Education is 54°. Consider the following pairs:
| 1. | Percentage expenditure on Food | 30% |
| 2. | Ratio of Food to Education expenditure | 2 : 1 |
| 3. | Total percentage of remaining sectors | 60% |
How many of the above pairs are correctly matched?
Answer: B
Only two pairs are correctly matched.
Convert each angle to a share of 360°.
\[ \begin{aligned} \text{Food} &= \tfrac{108}{360} \times 100 = 30\% \\ \text{Education} &= \tfrac{54}{360} \times 100 = 15\% \end{aligned} \]
Pair 1 (30%) is right. Pair 2 is right: 108 : 54 = 2 : 1. Pair 3 is wrong: the remaining sectors are \(100 - 30 - 15 = 55\%\), not 60%. 60% would need Education to be 10%, that is 36°, not 54°.
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