VeritasPrepKarishma wrote:
registerincog wrote:
School A is 40% girls and school B is 60% girls. The ratio of the number of girls at school A to the number of girls at school B is 4:3. if 20 boys transferred from school A to school B and no other changes took place at the two schools, the new ratio of the number of boys at school A to the number of boys at school B would be 5:3. What would the difference between the number of boys at school A and at school B be after the transfer?
A) 20
B) 40
C) 60
D) 80
E) 100
Algebra Solution
Say, if you do insist on algebra and do not want to rely on reasoning, try to work in a single variable.
Girls in A:Girls in B = 4:3
Girls in A = 4n, Girls in B = 3n
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n.
(6n - 20)/(2n + 20) = 5/3
You get n = 20
Boys at school A after transfer = 6*20 - 20 = 100
Boys are school B after transfer = 2*20 + 20 = 60
Difference = 40
Answer (B)
Responding to a pm:
Quote:
Can you please explain this part of your solution:
Since in A, girls are 40% and boys are 60%, number of boys is 6n.
Since in B, girls are 60% and boys are 40%, number of boys is 2n
Why is it that you didn't represent boys in school b as 4n? You simplified it 60/40 to get 3/2. However, in A you left the boys as 6n, you did not reduce the ratio as you did in B.
Your help would be greatly appreeciated.
Girls in A:Girls in B = 4:3
Assume actual numbers with a variable:
Girls in A = 4n, Girls in B = 3n
Since in school A, girls are 40% and boys are 60%,
40% of Total students in A = 4n
Total students in A = 4n *100/40 = 10n
So number of boys in school A = 10n - 4n = 6n
Using the same logic for school B, since in school B, girls are 60%,
60% of Total students in B = 3n
Total students in = 3n * 100/60 = 5n
So the number of boys in school B = 5n - 3n = 2n
I hope you understand from where I got 6n and 2n. I did this so that a single variable represents all the relevant quantities.
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