Problem Solving

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 ave 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


[spoiler]OA:B[/spoiler]

Hey there,

1st Year of the total [1/2]
2d Year of the total [1/2]
1st Year ND (Not Declared) [4/5]
1st Year D (Declared) [1- (4/5)] = [1/5]

2d Year D is 3x the 1st Year D. Thus, [1/5] * 3 = [3/5]
Then, 2d Yaer ND is (1 - [3/5]) = [2/5]
2d Year ND of the total is [2/5] * [1/2] = [2/10] = [1/5]

Any other ways?

i was not reading the q properly... my bad!!!
thanks.....

let x be the students in the darmitory

1/2 are first year students=1/2x

1/2 are the 2nd year students=1/2x

first year students not declared majors=(4/5)*x/2=

first year students declared majors are=x/2-4x/10=x/10

2nd year students who have majors is 3 times the first year students who have declared majors

so 3x/10 are the 2nd year students who have major

so the 2nd year students who have not declared a major is
x/2-3x/10=5x-3x/10=2x/10=x/5

(1/5)x

Answer is (B)

suggest me if iam wrong