edited by
651 views
1 votes
1 votes
In a class, $60\%$ of the students are girls and the rest are boys. There are $30$ more girls than boys. If $68\%$ of the students, including $30$ boys, pass an examination, the percentage of the girls who do not pass is _______
edited by

1 Answer

1 votes
1 votes

Let $100x$ be the total number of student in a class.

The girls are in a class $ = 60\% = 100x \times \frac{60}{100} = 60x $

And, the boys are in a class $ = 100\% – 60\% = 40\% = 100x \times \frac{40}{100} = 40x$

According to the question :

There are $30$ more girls than boys.

$ 60x = 40x + 30 $

$\Rightarrow 60x – 40x = 30$

$ \Rightarrow 20x = 30 $

$ \Rightarrow \boxed{x = \frac{3}{2}} $

The number of student in a class $ = 100x = 100 \times \frac{3}{2} = 150 $

Therefore,

  • The total number of girls in a class $ = 60x = 60 \times \frac{3}{2} = 90 $
  • The total number of boys in a class $ = 40x = 40 \times \frac{3}{2} = 60$

If $68\%$ of the students, including $30$ boys pass an examination.

Then, total number of students who passes in the exam (including $30$ boys) $ = 150 \times \frac{68}{100} = 102 $

Let $k$ be the number of girls who passed in the exam.

$ 30 \; \text{(Boys)} + k \; \text{(Girls)} = 102 $

$ \Rightarrow k = 102 – 30 $

$ \Rightarrow k = 72 $

The total number of girls in a class $ = 90 $

Therefore,

  • Number of girls who passed in the exam $ = 72 $
  • Number of girls who failed in the exam $ = 90 – 72 = 18 $

$ \therefore$ The percentage of the girls who failed in the exam$ = \frac{18}{90} \times 100 = 20\%.$

Correct Answer $: 20$

edited by
Answer:

Related questions

1 votes
1 votes
1 answer
1
go_editor asked Mar 8, 2020
613 views
The income of Amala is $20\%$ more than that of Bimala and $20\%$ less than that of Kamala. If Kamala's income goes down by $4\%$ and Bimala’s goes up by $10\%$, then t...
1 votes
1 votes
1 answer
2
2 votes
2 votes
1 answer
3
go_editor asked Mar 8, 2020
578 views
Let $\text{S}$ be the set of all points $(x,y)$ in the $x-y$ plane such that $|x|+|y|\leq 2$ and $|x|\geq 1$. Then, the area, in square units, of the region represented b...
2 votes
2 votes
1 answer
4
go_editor asked Mar 8, 2020
593 views
With rectangular axes of coordinates, the number of paths from $(1,1)$ to $(8,10)$ via $(4,6)$, where each step from any point $(x,y)$ is either to $(x,y+1)$ or to $(x+1,...
2 votes
2 votes
1 answer
5
go_editor asked Mar 8, 2020
516 views
Let T be the triangle formed by the straight line $3x+5y-45=0$ and T the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as ...