JEE MAIN - Mathematics (2002 - No. 2)
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?
73
65
68
74
Uitleg
Given that, total students = 100
and number of boys = 70
$$\therefore$$ No. of girls = 100 - 70 = 30
Average of 100 students = 72
$$\therefore$$ Total marks of 100 students = 100 $$ \times $$ 72 = 7200
Average of 70 boys = 75
$$\therefore$$ Total marks of 70 boys = 70 $$ \times $$ 75 = 5250
$$\therefore$$ Total marks of 30 girls = 7200 $$ - $$ 5250 = 1950
$$\therefore$$ Average marks of 30 girls = $${{1950} \over {30}}$$ = 65
and number of boys = 70
$$\therefore$$ No. of girls = 100 - 70 = 30
Average of 100 students = 72
$$\therefore$$ Total marks of 100 students = 100 $$ \times $$ 72 = 7200
Average of 70 boys = 75
$$\therefore$$ Total marks of 70 boys = 70 $$ \times $$ 75 = 5250
$$\therefore$$ Total marks of 30 girls = 7200 $$ - $$ 5250 = 1950
$$\therefore$$ Average marks of 30 girls = $${{1950} \over {30}}$$ = 65