The ratio of the number of students in two classrooms, `C_(1) and C_(2)`, is 2 : 3 . It is observed that after shifting ten students from ` C_(1) " to " C_(2)`, the ratio is 3 : 7. Further, how many students have to be shifted from ` C_(2)"to" C_(1)` for the new ratio to become 9 : 11 ?

Options

A. 10
B. 15
C. 20
D. 8

Answer

B

Explanation

(i) Consider the number of students in ` C_(1) and C_(2)` as 2x and 3x respectively.
(ii) Let the number of students in the two classes `C_(1) and C_(2)` be 2x and 3x respectively.
(iii) Given `(2x - 10) : (3x+10) = 3 : 7`.
Find x from this equation.
(iv) Let y be the number of students to be shifted from ` C_(2)" to "C_(1)`.
(v) Substitute value of x in `(2x - 10 + y) : (3x + 10 - y) = 9 : 11 ` and find y.