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The following table gives data of some students. However, some data has been spoilt and cannot be read on the computer floppy

It is also known that:

1. Half the students were either excellent or good.

2. 40% of the students were females

3. One-third of the male students were average. Based on the above answer the following questions.

How many students are both female and excellent?

- $0$
- $8$
- $16$
- $32$

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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 | $\color{blue}{10}$ | $\color{blue}{80}$ |