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Question

In a class, $$10%$$ of the girls have blue eyes, and $$20%$$ of the boys have blue eyes. If the ratio of girls to boys in the class is $$3:4$$, then what is the fraction of the students in the class having blue eyes?


A
11/70
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B
11/45
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C
14/45
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D
12/33
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E
23/49
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Solution

The correct option is A $${ 11 }/{ 70 }$$
  $$ \text{Let total number of students be 100} $$
 $$ \text{blue eyed boys =20/100} $$
 $$ \text{blue eyed girls =10/100} $$
 $$ ratio\,of\,girls\,to\,boys=3:4 $$
 $$ hence $$
 $$ Blue\text{ eye boys=}\dfrac{1}{5}\times \dfrac{4}{7}=\dfrac{4}{35} $$
 $$ Blue\,eye\,girls=\dfrac{1}{10}\times \dfrac{3}{7}=\dfrac{3}{70} $$
 $$ Fraction\text{ of students having blue eyes=}\dfrac{4}{35}+\dfrac{3}{70} $$
 $$ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\dfrac{11}{70} $$

Mathematics

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