Question : The pie chart given below shows the expenditure incurred by a person on 7 articles. The total expenditure of all these 7 articles is 720. Expenditure incurred on a particular article is shown in terms of degree concerning the total expenditure incurred in all these 7 articles.
What is the ratio of expenditure incurred on article A2 to expenditure incurred on article A7?
Option 1: 2 : 3
Option 2: 3 : 4
Option 3: 4 : 3
Option 4: 5 : 3
Correct Answer: 3 : 4
Solution :
Central angle of A2,
= $\frac{\text{Expenditure on A2}}{\text{Total Expenditure}}$
Central angle of A7, = $\frac{\text{Expenditure on A7}}{\text{Total Expenditure}}$
Since expenditure is directly proportional to the central angle
⇒ Required ratio = $\frac{\frac{\text{Expenditure on A2}}{\text{Total Expenditure}}}{\frac{\text{Expenditure on A7}}{\text{Total Expenditure}}}$ = $\frac{\text{Central angle of A2}}{\text{Central angle of A7}}$
⇒ Ratio = $\frac{15}{20}$ = $\frac{3}{4}$
Hence, the correct answer is 3 : 4.
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