Question

In an exam, $\frac{1}{4}$ of the students failed both in English and Maths, $35\%$ students failed in Maths and $30\%$ failed in English.
(i)Find the percentage of students who failed in any of the subjects.
(ii)Find the percentage of students who passed in both the subjects.
(iii)If the number of students who failed only in English was $25$, find the total number

Answer 1

Percentage of Students failed in both English and Math $=\frac{1}{4}\times 100=25\%$

$\left(1\right)$ $n\left(MuE\right)=n\left(E\right)+n\left(M\right)-n\left(Enm\right)$

$percentageof\left(MuE\right)$ $=30+35-25$

$=65-25$

$=40\%$

$\left(2\right)$ Percentage of students who passed in both the subjects

$=E^{\prime }n{M}^{\prime }$

$={\left(EuM\right)}^{\prime }$

$=100-40$

$=60\%$

$\left(3\right)$ let the total number of students be $x$ then

$30\%ofx=25$

$=\frac{30\times x}{100}=25$

$x=\frac{25\times 100}{30}$

$x=\frac{250}{3}$

$x=83.33$

$x=84$