Problem Solving

In a particular election, everyone votes for either candidate A or candidate B. After 60% of the votes are counted, candidate A is leading 60% to 40%. What percentage of the remaining votes must B get in order to have the same number of votes as A?

(a) 60
(b) 65
(c) 66 2/3
(d) 70
(e) 75

B = 65%

Bhattu wrote:B = 65%

yep .. I agree with Bhattu.

dtweah wrote:In a particular election, everyone votes for either candidate A or candidate B. After 60% of the votes are counted, candidate A is leading 60% to 40%. What percentage of the remaining votes must B get in order to have the same number of votes as A?

(a) 60
(b) 65
(c) 66 2/3
(d) 70
(e) 75

what's OA?

dtweah, can you please be considerate and keep the posts updated with the answers? You are posting great questions, but without answers.

Thx.

kanha81 wrote:

dtweah wrote:In a particular election, everyone votes for either candidate A or candidate B. After 60% of the votes are counted, candidate A is leading 60% to 40%. What percentage of the remaining votes must B get in order to have the same number of votes as A?

(a) 60
(b) 65
(c) 66 2/3
(d) 70
(e) 75

what's OA?

dtweah, can you please be considerate and keep the posts updated with the answers? You are posting great questions, but without answers.

Thx.

My apology. OA is B: Here is the official version.

(b) Let p be the fraction of the remaining votes needed by B. Then
.4x.6 + px.4 = .5 from which p = .65.

dtweah wrote:

kanha81 wrote:

dtweah wrote:In a particular election, everyone votes for either candidate A or candidate B. After 60% of the votes are counted, candidate A is leading 60% to 40%. What percentage of the remaining votes must B get in order to have the same number of votes as A?

(a) 60
(b) 65
(c) 66 2/3
(d) 70
(e) 75

what's OA?

dtweah, can you please be considerate and keep the posts updated with the answers? You are posting great questions, but without answers.

Thx.

My apology. OA is B: Here is the official version.

(b) Let p be the fraction of the remaining votes needed by B. Then
.4x.6 + px.4 = .5 from which p = .65.

No worries! I just did not know the answer. Thanks for the posting.

When I calculated, I got 66 2/3. This is how did-
Let n: total votes= 100
r: remaining votes

votes counted = 60% * (100) = 60
A is leading by 60% to 40%: 60% * (60) = 36 -> r = 60-36 = 24
40% (60) = 24 -> r=100-24 = 36

p% * (36) = 24
p = 66 2/3

kanha81 wrote:

dtweah wrote:

kanha81 wrote:

dtweah wrote:In a particular election, everyone votes for either candidate A or candidate B. After 60% of the votes are counted, candidate A is leading 60% to 40%. What percentage of the remaining votes must B get in order to have the same number of votes as A?

(a) 60
(b) 65
(c) 66 2/3
(d) 70
(e) 75

what's OA?

dtweah, can you please be considerate and keep the posts updated with the answers? You are posting great questions, but without answers.

Thx.

My apology. OA is B: Here is the official version.

(b) Let p be the fraction of the remaining votes needed by B. Then
.4x.6 + px.4 = .5 from which p = .65.

No worries! I just did not know the answer. Thanks for the posting.

When I calculated, I got 66 2/3. This is how did-
Let n: total votes= 100
r: remaining votes

votes counted = 60% * (100) = 60
A is leading by 60% to 40%: 60% * (60) = 36 -> r = 60-36 = 24
40% (60) = 24 -> r=100-24 = 36

p% * (36) = 24
p = 66 2/3

You began good by getting the 36 and 24. p% * (36) = 24 says some proportion of A's votes equal B's present vote, which is not what the question is asking. Try to interpret your equations whenver you write them and see if they conform to what the problem is asking . You should be applying the percentage to the remaining votes not to A's. The beginning was good but you misapplied later on. Try several more and you will get it.

Practice putting mathematical sentences into equation. This is the most important part of the problem. The rest is arithmetic.

dtweah wrote: (b) Let p be the fraction of the remaining votes needed by B. Then
.4x.6 + px.4 = .5 from which p = .65.

Can you please clarify this OE?

In order to find the % of votes that B must require to equal A-

p * 0.4, where 0.4 is remaining uncounted votes +
0.6 * 0.4, where 0.6 is 60% of counted votes and 0.4 is 40% of counted votes
=
0.5, where 0.5 is a+b=n --> 2b=n ---> b = n * 0.5

So, does the actual equation look like?

100 (p * 0.4 + 0.6 * 0.4 ) = 0.5 * 100

I don't know if I am understanding this question correctly or not!

kanha81 wrote:

dtweah wrote: (b) Let p be the fraction of the remaining votes needed by B. Then
.4x.6 + px.4 = .5 from which p = .65.

Can you please clarify this OE?

In order to find the % of votes that B must require to equal A-

p * 0.4, where 0.4 is remaining uncounted votes +
0.6 * 0.4, where 0.6 is 60% of counted votes and 0.4 is 40% of counted votes
=
0.5, where 0.5 is a+b=n --> 2b=n ---> b = n * 0.5

So, does the actual equation look like?

100 (p * 0.4 + 0.6 * 0.4 ) = 0.5 * 100

I don't know if I am understanding this question correctly or not!

B's current vote + percent of vote B needs of remaining = half of all votes counted

The problem wants be to get 36 votes which A has currently. But while B is getting 36, A is not remaining at 36. His votes will be increasing. So the only way B can get 36 is if B gets half of the votes.

Another way to see is

P%40 +24=(1-P%)40 +36. Here you get the percentage of remaining votes each will get and add to their respective current votes and equate. The trick or difficulty in problem is to see that you have to equate.
p% 40 +24= 40 -P%40 +36
P% 40 +P%40 =52. Just see p% as x and don't multiply by 100. 40x+40x=80x.

80P%=52
P%=52/80=.65

Hope this perspective helps.

Finally A and B should get equal number of votes i.e. 50% each

B has already got 40%(60%) = 24% of the votes.

So from the remaining 40% of the votes he must get 26%.

Thus the required percentage is 26/40 x 100 = 65%

sureshbala wrote:Finally A and B should get equal number of votes i.e. 50% each

B has already got 40%(60%) = 24% of the votes.

So from the remaining 40% of the votes he must get 26%.

Thus the required percentage is 26/40 x 100 = 65%

Thank you dtweah for taking time to explain.

Thank you Sureshbala. Makes more sense now.

Just when I thought I have figured out this problem, this problem sprung its colors by showing the trickiness.