Question : The pie chart given below shows the number of boys in 8 schools. The total number of boys in all these 8 schools is 10000. The number of boys in a particular school is shown as a percent of the total number of boys in all these 8 schools.
What is the ratio of the central angle formed by sectors C, D, and F together to the central angle formed by sectors A, G, and H together?
Option 1: 19 : 44
Option 2: 17 : 39
Option 3: 20 : 43
Option 4: 44 : 21
Correct Answer: 20 : 43
Solution :
Use the formula, $\text{Required angle}=\frac{\text{Percent of sector}}{100}\times 360º$
The angle of the sectors,
C = $\frac{12}{100}\times 360º$ = 43.2º
D = $\frac{2}{100}\times 360º$ = 7.2º
F = $\frac{6}{100}\times 360º$ = 21.6º
The central angle formed by sectors C, D, and F together = 43.2º + 7.2º + 21.6º = 72º
The angle of the sectors,
A = $\frac{19}{100}\times 360º$ = 68.4º
G = $\frac{14}{100}\times 360º$ = 50.4º
H = $\frac{10}{100}\times 360º$ = 36º
The central angle formed by sectors A, G, and H together = 68.4º + 50.4º + 36º = 154.8º.
The ratio of the central angle formed by sectors C, D, and F together to the central angle formed by sectors A, G, and H together = 72º : 154.8º = 20 : 43.
Hence, the correct answer is 20 : 43.
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