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If the ratio of A to B is is 2 to 3 and the ratio of B to C

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Senior Manager
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If the ratio of A to B is is 2 to 3 and the ratio of B to C [#permalink] New post 11 Jan 2008, 09:27
If the ratio of A to B is is 2 to 3 and the ratio of B to C is 5 to 4, what is the triple ratio of A to b to C?


I did:

A/B =2/3, so 3A=2B and 6A=4B
B/C = 5/4, so 4B=5C

So we have 6A=4B=5C and the triple ratio is 6:4:5

Nevertheless, this reasoning is wrong. Can you say me WHY?
Regards
Director
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Re: Triple ratio [#permalink] New post 11 Jan 2008, 09:37
netcaesar wrote:
So we have 6A=4B=5C and the triple ratio is 6:4:5


if u look at the above logic, you will realise where you have gone wrong.

6a=4b=5c. Just looking at it, ranking from large to small, one would think the order is B>C>A

now looking at 6:4:5,

A > C > B.

i.e you cannot just convert 6A=4B=5C to 6:4:5.


Here is how I solved the problem

A B C
2 : 3
5 : 4


make the denominator of A:B to the numerator of B:C

ie

A B C
10:15
15 : 12

so you get A:B:C = 10:15:12
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Re: Triple ratio [#permalink] New post 11 Jan 2008, 09:58
A:B = 2:3
B:C = 5:4

Very simple: all we need to find is a common multiple of the two Bs (3 and 5). 15 is the LCM so we just multiple each equation to get the Bs equal to 15.

2:3 = 2*5:3*5 = 10:15
5:4 = 5*3:4*3 = 15:12

Now combine them because they're all on the same scale (both Bs = 15)

Triple Ratio: 10:15:12
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Re: Triple ratio [#permalink] New post 11 Jan 2008, 10:46
Thanks.

I made a big mistake!!!!!!!

I hope not to repeat it doing the exam.

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Re: Triple ratio [#permalink] New post 11 Jan 2008, 11:28
netcaesar wrote:
If the ratio of A to B is is 2 to 3 and the ratio of B to C is 5 to 4, what is the triple ratio of A to b to C?


I did:

A/B =2/3, so 3A=2B and 6A=4B
B/C = 5/4, so 4B=5C

So we have 6A=4B=5C and the triple ratio is 6:4:5

Nevertheless, this reasoning is wrong. Can you say me WHY?
Regards


Note that if 6A = 4B, A:B is not 6/4 but rather 4/6


Since A/B=2/3=10/15, and B/C=5/4=15/12, we get A:B:C=10:15:12
Re: Triple ratio   [#permalink] 11 Jan 2008, 11:28
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If the ratio of A to B is is 2 to 3 and the ratio of B to C

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