Question

# The average age of a class is $$15.8$$ years. The average age of the boys in the class is $$16.4$$ years while that of the girls is $$15.4$$ years. What is the ratio of boys to girls in the class?

A
1:2
B
2:3
C
3:4
D
3:5

Solution

## The correct option is B $$2 : 3$$Let the number of boys and girls in the class be $$x$$ and $$y$$ respectively.Total age of the class $$= 15.8 \times (x + y)$$$$=(15.8 x + 15.8y)$$ yearsTotal age of the boys $$= 16.4 x$$ yearsTotal age of girls $$= 15.4 y$$ years$$\therefore 16.4x + 15.4y = 15.8 x + 15.8y$$$$\Rightarrow 16.4 x - 15.8 x = 15.8y -15.4 y$$$$\Rightarrow 0.6x = 0.4 y$$$$\Rightarrow \displaystyle \frac{x}{y} = \frac{4}{6} = \frac{2}{3}$$Mathematics

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