Question

Out of the total $390$ students studying in a college of Arts and Science, boys and girls are

in the ratio of $7:6$ respectively and the number of students studying Arts and Science

are in the ratio of $3:7$ respectively. The boys and girls studying Arts are in the ratio of

$4:5$ respectively.

What is the ratio between the girls studying Arts and Science respectively?

• A. $13:23$
• B. $26:79$
• C. $8:13$
• D. $23:36$

Answer 1

The correct option is A $13:23$

Given, boys and girls are in the ratio of $7:6$,

So, Number of boys $=\frac{7}{13}\times 390=210$

Number of girls $=390-210=180$

Students studying Arts and Science are in the ratio of $3:7,$

Number of students studying Arts $=\frac{3}{10}\times 390=117$

Number of students studying Science $=390-117=273$

Also boys and girls studying Arts are in the ratio of $4:5,$

Number of girls studying arts $=\frac{5}{9}\times 117=65$

Number of girls studying science $=180-65=115$

Then, the ratio of girls studying in arts and science $=\frac{65}{115}=\frac{13}{23}$