Of all the students in a certain dormitory, 1 2 are first-year students and the rest are second-year students. If 4 5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 3 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?

A. 1/15B. 1/5C. 4/15D. 1/3E. 2/5

(B) 1/5

Step-by-step explanation:

First year student = 1/2 of the students in a certain dormitory. = x

Second year student = 1/2 of the students in a certain dormitory. = x

First year = second year = x

Total students in the dormitory = x+x = 2x

4/5 of the first year students have not declared a major = 4/5x

first year students who have declared a major = x - 4/5x = 1/5x

Second year student who has declared a major is 3 times the fraction of the first year student who have declared major = 3/5x

Second year student who have not declared major = x - 3/5x = 2/5x

The fraction of all the students in the dormitory are second-year students who have not declared a major = (2/5x) / 2x

= 2x/5 * 1/2x

= 1/5