Question

In an examination out of 900 students 85% of the boys and 70% of girls passed. How many girls appeared in the examination, if the total pass percentage was 75%?

Answer 1

Hint: Here we go through by dividing the 900 students in categories of boys and girls by letting the number of girls be ‘x’ then automatically the number of boys becomes 900-x. Then apply the given percentage on these numbers according to the question to find unknown terms.

Complete step-by-step answer:
Here in the question it is given that the total number of students is 900.
Let the number of girls be x out of 900 students then automatically the number of boys students become 900-x.
According to the question,
 85% of boys passed the examination i.e. 85% of (900-x)$ = \dfrac{{85}}{{100}} \times (900 - x)$, as we assumed above that the number of boys are (900-x)
And 70% of girls passed the examination i.e. 70% of x$ = \dfrac{{70}}{{100}} \times x$ , as we assumed above that the number of girls are x.
Now in the question it is also given that the total pass percentage was 75% i.e. 75% 0f 900$ = \dfrac{{75}}{{100}} \times 900$
 It means that,
$
   \Rightarrow \dfrac{{85}}{{100}} \times (900 - x) + \dfrac{{70}}{{100}} \times x = \dfrac{{75}}{{100}} \times 900 \\
   \Rightarrow 85 \times 900 - 85x + 70x = 75 \times 900 \\
   \Rightarrow 15x = 900(85 - 75) \\
   \Rightarrow x = \dfrac{{900}}{{15}} \times 10 = 600 \\
 $
And above we assume that ‘x’ is the number of girl students.
Therefore 600 girls have written the examination.

Note: Whenever we face such a type of question the key concept for solving the question is whenever in the question if sum of two things are given then assume the one thing with a variable then for the number of other things it automatically becomes total minus that variable. Then apply the given condition of question to that number which we assume and by doing this we will find the unknown term and by this we easily get our answer.