Let's start with fill the gaps in table:
|
|
Performance |
|
Total |
|
Average |
Good |
Excellent |
|
Male |
|
|
10 |
|
Female |
|
|
|
32 |
Total |
|
30 |
|
|
We know that Total female students = 32
$40\%$ of the total students were females.
$∴ \text{Total students} = \dfrac{32 \times 100}{40} = 80$
|
|
Performance |
|
Total |
|
Average |
Good |
Excellent |
|
Male |
|
|
10 |
|
Female |
|
|
|
32 |
Total |
|
30 |
|
$\color{blue}{80}$ |
$∴\text{Total Male students = (80-32) = 48}$
|
|
Performance |
|
Total |
|
Average |
Good |
Excellent |
|
Male |
|
|
10 |
$\color{blue}{48}$ |
Female |
|
|
|
32 |
Total |
|
30 |
|
$\color{blue}{80}$ |
$\dfrac{1}{3}^{rd} \text{of the male students =} \{(\dfrac{1}{3}\times 48) = 16\}\text{ were average}$
|
|
Performance |
|
Total |
|
Average |
Good |
Excellent |
|
Male |
$\color{blue}{16}$ |
|
10 |
$\color{blue}{48}$ |
Female |
|
|
|
32 |
Total |
|
30 |
|
$\color{blue}{80}$ |
$∴\text{ Good male students = 48 - (16+10)= 22}$
$∴\text{ Good female students = 30 - 22 = 8}$
|
|
Performance |
|
Total |
|
Average |
Good |
Excellent |
|
Male |
$\color{blue}{16}$ |
$\color{blue}{22}$ |
10 |
$\color{blue}{48}$ |
Female |
|
$\color{blue}{8}$ |
|
32 |
Total |
|
30 |
|
$\color{blue}{80}$ |
Now, we know that half of the students i.e. $\dfrac{80}{2} = 40$ students were either excellent or good.
∴ Rest $(80-40)=40$ students were average
|
|
Performance |
|
Total |
|
Average |
Good |
Excellent |
|
Male |
$\color{blue}{16}$ |
$\color{blue}{22}$ |
10 |
$\color{blue}{48}$ |
Female |
$\color{blue}{(40-16) = 24}$ |
$\color{blue}{8}$ |
|
32 |
Total |
$\color{blue}{40}$ |
30 |
|
$\color{blue}{80}$ |
∴ $\color{green}{\text{There are}}$ $\color{red}{no}$ $\color{green}{\text{female students who are excellent.}}$
|
|
Performance |
|
Total |
|
Average |
Good |
Excellent |
|
Male |
$\color{blue}{16}$ |
$\color{blue}{22}$ |
10 |
$\color{blue}{48}$ |
Female |
$\color{blue}{(40-16) = 24}$ |
$\color{blue}{8}$ |
-- |
32 |
Total |
$\color{blue}{40}$ |
30 |
$\color{blue}{10}$ |
$\color{blue}{80}$ |