selango wrote:Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student come in. What fraction of all students took biology and took chemistry?

A. 7/9

B .6/7

C.5/7

D.4/9

E.2/5

OA A

From the info we have

Biology Chemistry Physics
1/2 1/3 1/6
Lets take total as 12 => 6 4 2
Students left = (1/2)*6 (1/4)*4 -
Students remaining = 4 3 2

Fraction of students who took Biology and Chemistry = (no. of students in Biology & Physics)/(total no. of students)
= (4+3)/(9)
= 7/9

Every student of a certain school must take one and only one elective course. In last year, 1/2 of the students took biology as an elective, 1/3 of the students took chemistry as an elective, and all of the other students took physics. In this year, 1/3 of the students who took biology and 1/4 of the students who took chemistry left school, other students did not leave, and no fresh student come in. What fraction of all students took biology and took chemistry?

N/2 = B
N/3 = C
N/6 = P

1/3 *N/2 = N/6 left
1/4 * N/3 = N/12 left
Total N/4

So remaining are 3N/4
3N/4-N/6 = 7N/12

Hence fraction = 7N/12 / 3N/4
=7/9

let us assume the total students = 120
1/2 biology = 60
1/3 chemistry=40
physics=20

left students =30
1/3 of biology= 20
1/4 of chemistry=10


Ratio :(60-20+40-10)/(120-30)=70/90

A