Average age of students of a class is 15.8 ,years. average age of boys in class is 16.4 years and th

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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

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