The boys and girls in a college are in the ratio 3 : 2. If 20% of the boys and 25% of the girls are adults, the percentage of students who are not adults is -

Solution(By Examveda Team)

Let the number of boys and girls be 3x and 2x respectively
Then,
Number of boys and girls who are adults
$$\eqalign{ & = 20\% {\text{ of }}3x + 25\% {\text{ of }}2x \cr & = \left( {\frac{{20}}{{100}} \times 3x} \right) + \left( {\frac{{25}}{{100}} \times 2x} \right) \cr & = \frac{3}{5}x + \frac{x}{2} = \frac{{11x}}{{10}} \cr} $$
∴ Number of boys and girls who are not adults
$$\eqalign{ & = \left[ {\left( {3x + 2x} \right) - \frac{{11x}}{{10}}} \right] \cr & = 5x - \frac{{11x}}{{10}} \cr & = \frac{{39x}}{{10}} \cr & {\text{Required percentage}} \cr & = \left( {\frac{{39x}}{{10}} \times \frac{1}{{5x}} \times 100} \right)\% \cr & = 78\% \cr} $$