Why divide by 20 while finding number of female students in civil and mechanical?

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17 votes

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year $2012$. The proportion of male to female students in each department is $5:4$. There are $40$ males in Electrical Engineering. What is the difference between the numbers of female students in the civil department and the female students in the Mechanical department?

21 votes

Best answer

Number of female students in Electrical = $40\times \dfrac{4}{5} = 32$

Number of female students in Civil = $32\times \dfrac{30}{20} = 48$ (Since proportion of male students to female students is same, the breakup chart is the same for number of female students)

Number of female students in Mechanical = $32\times \dfrac{10}{20} = 16$

So, answer = $48 - 16 = 32$

Number of female students in Civil = $32\times \dfrac{30}{20} = 48$ (Since proportion of male students to female students is same, the breakup chart is the same for number of female students)

Number of female students in Mechanical = $32\times \dfrac{10}{20} = 16$

So, answer = $48 - 16 = 32$

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24 votes

Electrical male students = 40

∴ Electrical female students = 40 × (4/5)= 32

Total no. of students in Electrical department = (40 + 32) = 72 (which is 20% of the total mass)

∴ Total no. of students in the college = 72 × (100/20) = 360

Total no. of students in Civil department = 360 × (30/100) = 108

Civil female students = 108 × (4/9) = 48

Total no. of students in Mechanical department = 360 × (10/100) = 36

Mechanical female students = 36 × (4/9) = 16

∴ Difference = (48 − 16) = 32 (Ans)

∴ Electrical female students = 40 × (4/5)= 32

Total no. of students in Electrical department = (40 + 32) = 72 (which is 20% of the total mass)

∴ Total no. of students in the college = 72 × (100/20) = 360

Total no. of students in Civil department = 360 × (30/100) = 108

Civil female students = 108 × (4/9) = 48

Total no. of students in Mechanical department = 360 × (10/100) = 36

Mechanical female students = 36 × (4/9) = 16

∴ Difference = (48 − 16) = 32 (Ans)