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another weighted average problem

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by rahul.s » Wed Feb 10, 2010 5:24 am
last year, all registered voters in country X voted for either A or B. this year, the number of A voters increased by 10%, while the total number of B voters increased 5%. no other votes were cast. if the number of total voters increased 8% what fraction of the voters voted for A this year?

[spoiler]OA is 11/18[/spoiler]
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by shashank.ism » Wed Feb 10, 2010 5:48 am
rahul.s wrote:last year, all registered voters in country X voted for either A or B. this year, the number of A voters increased by 10%, while the total number of B voters increased 5%. no other votes were cast. if the number of total voters increased 8% what fraction of the voters voted for A this year?

[spoiler]OA is 11/18[/spoiler]
Initial no. for A = A, no. for B = B , no. toatal = A+B
now
no. of A = 1.1A
no. of B=1.05 B
total no. of voters = 1.08 (A+B)
1.08 (A+B) = 1.1A+1.05B ->0.03B= 0.02A --> 3B=2A
so fraction of A = 1.1A/(1.08(A+B)=[spoiler]11/18[/spoiler]
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by thephoenix » Wed Feb 10, 2010 5:53 am
rahul.s wrote:last year, all registered voters in country X voted for either A or B. this year, the number of A voters increased by 10%, while the total number of B voters increased 5%. no other votes were cast. if the number of total voters increased 8% what fraction of the voters voted for A this year?

[spoiler]OA is 11/18[/spoiler]
last year let voters for A=a and that for B=b
tot=a+b

this year voters for A=1.1a and that for B=1.05b
tot=1.1a+1.05b.....eqn1

this year tot=1.08 last year total
so eqn is
1.1a+1.05b=1.08(a+b)---->0.02a=0.03b--->b=2a/3

put b in eqn1 t=1.8a

so fraction of voters for A this year=1.1a/1.8a=11/18
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by bhumika.k.shah » Wed Feb 10, 2010 10:23 am
hey rahul,

i dont know how this is a weighted average problem .

But with two equations and two variables u can get the values of A and B .

The phoenix has solved it quite well . :)

Do let me know if u need any further clarification

Happy to help :)
rahul.s wrote:last year, all registered voters in country X voted for either A or B. this year, the number of A voters increased by 10%, while the total number of B voters increased 5%. no other votes were cast. if the number of total voters increased 8% what fraction of the voters voted for A this year?

[spoiler]OA is 11/18[/spoiler]
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by shashank.ism » Wed Feb 10, 2010 10:36 am
bhumika.k.shah wrote:hey rahul,

i dont know how this is a weighted average problem .

But with two equations and two variables u can get the values of A and B .

The phoenix has solved it quite well . :)

Do let me know if u need any further clarification

Happy to help :)
rahul.s wrote:last year, all registered voters in country X voted for either A or B. this year, the number of A voters increased by 10%, while the total number of B voters increased 5%. no other votes were cast. if the number of total voters increased 8% what fraction of the voters voted for A this year?

[spoiler]OA is 11/18[/spoiler]
Its a simple algebra problem. You can think of it logically in terms of %ge increase and decrease similar to problem of profit and loss and u will get to the correct answer.
You can also make two equations out of it and solve it easily.
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