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PS tough question !

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by meng » Wed Jan 28, 2009 12:37 pm
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
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by DanaJ » Wed Jan 28, 2009 1:07 pm
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.
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by coffee5251 » Wed Jan 28, 2009 4:36 pm
DanaJ wrote:This means that s/4 = 30 or that s = 120.

IMO answer is D.
Do you mean E (120)?
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by DeepakR » Wed Jan 28, 2009 7:26 pm
Yes its E - 120. J/S=3/4 and (J-10)/(S-20)=4/5 on solving both we get S=120
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by DanaJ » Wed Jan 28, 2009 10:14 pm
Ooops... Sorry... Yes, the correct answer is 120....
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