1.

The students of a university were classified according to faculty and gender. 60 % of total 40,000 students were boys. The number of girls in engineering faculty was three times the number of girls in commerce faculty. 15% and 10% of the total number of university students were boys and girls respectively who belonged to medical faculty. 20 % of the total number of students in the university belonged to faculty of science and among these students, the number of girls were one-seventh of the number of boys. 7% and 17% of the total number of students of arts faculty were boys and girls respectively. 3.75 % of the total number of students of the university belonged to the commerce faculty and the proportion of boys and girls among them was 3: 7. Present the above data in an appropriate table.

Answer»

In the given data two attributes are :

  1. Faculty: Engineering, Medical, Science, Arts, Commerce
  2. Sex: Boys, Girls

According to these two attributes table is prepared as follows :
Table showing the number of students of a university according to their faculties and sex

FacultySexTotal no. of students
BoysGirls
Engineering7750315010900
Medical6000400010000
Science700010008000
Arts280068009600
Commerce45010501500
Total no. of students240001600040000

Explanation:

No. of boys = 40000 × 60100 = 24000
No. of girls = (40000 – 24000 =) 16000

No. of girls in medical faculty = 40000 × 10100 = 4000
= 4000 and No. of boys = 40000 x 15100 = 6000
∴ No. of students in medical faculty = (4000 + 6000) = 10000

No. of students in Science faculty
= 40000 × 20100 = 8000

Suppose, the number of boys = x = 7000
∴ No. of girls = x7 = 1000

Now, x + x7 = 8000
x = 7000
∴ No. of boys in Arts faculty = 40000 × 7100
= 2800
and No. of girls = 40000 x -yyr = 6800
∴ The number of students in Arts faculty = 2800 + 6800 = 9600
No. of students in commerce faculty = 40000 × 17100 = 1500

∴ The number of students In Arts faculty = 2800 + 6800 = 9600
No. of students in commerce faculty = 40000 × 3.75100 = 1500

The proportion of boys and girls is 3:7.
∴ No. of boys = 310 × 1500 = 450
No. of girls = 710 × 1500 = 1050

No. of girls in Engineering faculty
= 3(1050)
= 3150

No. of boys
= 24000 – (6000 + 7000 + 2800 + 450)
= 24000- 16250 = 7750

∴ The number of students in Engineering faculty
= 7750 + 3150 = 10900


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