Question : The following pie chart shows the data regarding the donors of A, B, O, and AB blood groups.
The ratio of the number of donors of blood group ' $O$ ' to the average of the number of donors of blood groups ' $\mathrm{A}$ ' and ' $\mathrm{AB}$ ' together is:
Option 1: 2 : 3
Option 2: 1 : 1
Option 3: 2 : 1
Option 4: 1 : 2
Correct Answer: 1 : 1
Solution :
Let the total number of donors be $a$.
Number of donors of blood group '$O$' = $\frac{80°}{360°}\times a$
Number of donors of blood group '$A$' = $\frac{90°}{360°}\times a$
Number of donors of blood group '$AB$' = $\frac{70°}{360°}\times a$
Average of the number of donors of blood groups ' $\mathrm{A}$ ' and ' $\mathrm{AB}$ ' together
= $\frac{1}{2}\times ( \frac{90°}{360°}\times a+\frac{70°}{360°}\times a)$
= $\frac{80°}{360°}\times a$
So, the Ratio of the number of donors of blood group ' $O$ ' to the average of the number of donors of blood groups ' $\mathrm{A}$ ' and ' $\mathrm{AB}$ ' together = $\frac{80°}{360°}\times a:{\frac{80°}{360°}\times a}$ = 1 : 1
Hence, the correct answer is 1 : 1.
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