JEE MAIN - Mathematics (2007 - No. 1)
The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys
and girls combined is 50. The percentage of boys in the class is
80
60
40
20
Paliwanag
Let x and y are number of boys and girls in a class respectively.
$$\therefore$$ 52x + 42y = 50 (x + y)
$$ \Rightarrow$$ 52x + 42y = 50x + 50y
$$ \Rightarrow$$ 2x = 8y
$$ \Rightarrow$$ x = 4y
$$\therefore$$ Total no. of students = x + y = 4y + y = 5y
$$\therefore$$ Percentage of boys = $${{4y} \over {5y}} \times 100\,\% $$ = 80%
$$\therefore$$ 52x + 42y = 50 (x + y)
$$ \Rightarrow$$ 52x + 42y = 50x + 50y
$$ \Rightarrow$$ 2x = 8y
$$ \Rightarrow$$ x = 4y
$$\therefore$$ Total no. of students = x + y = 4y + y = 5y
$$\therefore$$ Percentage of boys = $${{4y} \over {5y}} \times 100\,\% $$ = 80%