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At a certain stage of a soccer tournament, the score ratio [#permalink]

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01 Dec 2012, 06:28

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At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

1)8 2)10 3)20 4)40 5)80

I tried this as below:

a:b:c = 3:4:5

a:b= 3:4

doubled: a:b = 2* 3:4 = 3:2

halved a:c = (1/2)*3:5 = 3:10

a:c/a:b = (3/10)/ (3/2) = 6/30

given c =40

substituting, we get b = 8.

Pls let me know the basic approach on this.

A to B = 3 : 4

So, on doubling we get 6 : 4

A to C = 3 : 5

So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20

So final ratio = 6 : 4 : 20.

If 20x = 40

4x = 8

Hence, answer is A
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Re: At a certain stage of a soccer tournament, the score ratio [#permalink]

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22 Mar 2016, 12:16

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At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

Ratio of A:B is originally 3:4. Then this ratio is doubled and we have \(\frac{3}{2}\) * 2 = \(\frac{6}{4}\) Ratio of A:C is originally 3:5. Then this ratio is halved so we have \(\frac{3}{5}\) * \(\frac{1}{2}\) = \(\frac{3}{10}\).

In order to compare the two ratio we must express the common term (in this case A) in the same quantity. Thus we multiply the second ratio (\(\frac{3}{10}\)) for 2 and we get \(\frac{6}{20}\)

So now the new score ratio of team A, B and C is 6:4:20. If we divide the score of team C by the ratio for team C we get the multiplier (in this case is 2). Finally by applying the multiplier to B we get 8.

At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

a) 8 b) 10 c) 20 d) 40 e) 80

Merging topics. Please refer to the discussion above.
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Re: At a certain stage of a soccer tournament, the score ratio [#permalink]

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12 Mar 2017, 10:49

I like making it in a table:

A:B:C 3:4:5 then A:B doubled 6:4:? then A:C halved 3:?:10 let's make a common ration for all 3: 6:4:20 and since C earned 40 points: 12:8:40 B is 8 Answer is A (8)

At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score of team B?

1)8 2)10 3)20 4)40 5)80

We are given that the original ratio of A : B : C = 3x : 4x : 5x.

After the ratio of A to B doubles and the ratio of A to C is halved, we have:

A/B = 6x/4x

AND

A/C = 3x/10x

Since we need term A to be the same in both ratios, we can multiply our second ratio by 2/2 and we have:

A/C = 6x/20x

Now the ratio of A : B : C = 6x : 4x : 20x

Since team C had a final of 40 points, we have:

20x = 40

x = 2

So, the final score of team B was 4 x 2 = 8.

Answer: A
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