msand
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. 1/15
B. 1/5
C. 4/15
D. 1/3
E. 2/5
Let all student of the dormitory = 120
First-year student = 60
Second year student= 60
Students of first year who declared major \(= (1-\frac{4}{5})=\frac{1}{5}\) \(=60*\frac{1}{5 }= 12\)
Students of the second year who declared major \(= 12*3=36\)
Student of the second year, who didn't declare major \(= 60-36=24\)
\(\frac{second-year \ students \ who \ have \ not \ declared \ a \ major}{Total \ students of \ the \ dormitory} = \frac{24}{120}=\frac{2}{10}=\frac{1}{5}\)
The answer is \(B\)