Problem Solving

Hi all,

I found this question is tough .. can anyone help me to solve it
and explain the answer for me plz


At the beginning of the year, the ratio of juniors to seniors in high school X was 3 to 4. During the year, 10 juniors and twice as many seniors transferred to another high school, while no new students joined high school X. If, at the end of the year, the ratio of juniors to seniors was 4 to 5, how many seniors were there in high school X at the beginning of the year?

a) 80
b) 90
c) 100
d) 110
e) 120

Let's say we have j = number of juniors and s = number of seniors. You get that j/s = 3/4. This means that j = 3s/4. Then you get some transfers which lead to the following equations:
(j - 10)/(s - 20) = 4/5. Substitute j with 3s/4 and you get that (3s/4 - 10)/(s - 20) = 4/5 or that 15s/4 - 50 = 4s - 80. This means that s/4 = 30 or that s = 120.

IMO answer is D.

DanaJ wrote:This means that s/4 = 30 or that s = 120.

IMO answer is D.

Do you mean E (120)?

Yes its E - 120. J/S=3/4 and (J-10)/(S-20)=4/5 on solving both we get S=120

Ooops... Sorry... Yes, the correct answer is 120....