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4.Average
hard
The average age of students of a class is $15.8 \,years.$ The average age of boys in the class is $16.4$ $years$ and that of the girls is $15.4\, years.$ The ratio of number of boys to the number of girls in the class is:
A
$1: 2$
B
$3: 4$
C
$3: 5$
D
$2: 3$
Solution
Let, the number of boys be $x$ and the number of girls be $y.$
Sum of ages of boys $=16.4 x$
Sum of ages of girls $=15.4 y$
The average age of all the students
$=\frac{16.4 x+15.4 y}{x+y}=15.8$
$\Rightarrow 16.4 x+15.4 y=15.8 x+15.8 y$
or, $16.4 x-15.8 x=15.8 y-15.4 y$
or, $0.6 x=0.4 y$
or, $\frac{x}{y}=\frac{0.4}{0.6}=\frac{2}{3}$ or $x y=2:3$
Standard 13
Quantitative Aptitude
