Question : The ratio of the number of boys to girls in a village is 3 : 2. If 30% of boys and 70% of girls appeared in an examination, the ratio of the number of villagers who appeared in the examination to that not appeared in the same examination is:
Option 1: 9 : 14
Option 2: 23 : 27
Option 3: 1 : 1
Option 4: 27 : 23
Correct Answer: 23 : 27
Solution :
The ratio of the number of boys to that of girls in a village = 3 : 2
Let the number of boys be $3x$ and number of girls be $2x$.
Number of boys appeared in the examination = $3x × 0.3 = 0.9x$
Number of girls appeared in the examination = $2x × 0.7 = 1.4x$
Ratio of numbers of villagers appeared : Ratio of villagers not appeared
= (0.9 + 1.4) : (5 – (0.9 + 1.4))
= 2.3 : 2.7
= 23 : 27
Hence, the correct answer is 23 : 27.
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