Question

In a school, 3/4 of the students study a language. Of those who study a language, 3/5 study French. Find the ratio of students who study French to students who do not study French. Give your answer in its simplest form.

Answer 1

Answer: 9:11

Explanation:

Let x be the total number of students.

If 3/4 of students study a language That mean 3x/4 students study a language.

Number of students that don't study a language becomes

x - 3x/4 = x/4.

and 3/5 of those who study language study French, that means 3x/4 * 3/5 of students study French.

This gives 3x/4 * 3/5 = 9x/20 Studying French.

Number of students that study language but do not study French becomes

3x/4 - 9x/20 = 6x/20

Total number of students that do not study French becomes

[total number of students not studying any language] + [total number of students studying a language but do not study French ]

Which becomes

x/4 + 6x/20 = 11x/20

Hence ratio of those that study French to those that do not study French Becomes

9x/20 : 11x/20

9:11.