Question

Preeti and Aashmi fought the election for the post of head girl of the school, for which the students of classes ${10}^{th}$, ${11}^{th}$ and ${12}^{th}$ voted. If three-seventh of the students voted for Preeti only three-seventh for Aashmi fifty for both and $50$ students did not use their votes, find the number of students, who voted for Preeti.

Answer 1

Let the total number of students in class${10}^{th}$, ${11}^{th}$ and ${12}^{th}$ be x then

Number of students voted for Preeti =$\frac{3}{7}x$

Number of students voted for Aashmi =$\frac{3}{7}x$

Number of students who did not use their votes $=50$

$x=\frac{3}{7}$ x + $\frac{3}{7}x+50$

$x=\frac{6}{7}x+50$

$x-\frac{6}{7}x=50$

$\frac{1}{7}x=50$

$x=50\times 7$

The total number of students in class ${10}^{th}$, ${11}^{th}$ and ${12}^{th}=350$

So the total number of students who voted for Preeti and who did not use their votes will be

= $(\frac{3}{7}\times 350)+50$

=$150+50$

Ans. 200 students