# Thread: Ratios: Combinining A:B , C:D to yield A:B:C:D.

1. ## Ratios: Combinining A:B , C:D to yield A:B:C:D.

Greetings to All!

This is my very first post on a Math forum. I am studying for GRE and there's one particular problem type on ratios which confuses me totally.. Multiple ratios combining..

Say I have two ratios with me

A : B => 21:23
C : D => 9:7

How do I determine A : B : C : D?

Sincerely,
Abhijit.

2. No, unless you are given more information, you won't be able to find A:B:C: D.

I could very well have A:B = 1:2 and also C: D = 1:2, but where A = 2, B = 4, C = 3, D = 6. THe ratio stilll holds, but you cannot directly find A:B:C: D unless you have something to compare one of each of the ratios given.

3. ## Re: Ratios: Combinining A:B , C:D to yield A:B:C:D.

Originally Posted by Unknown008
No, unless you are given more information, you won't be able to find A:B:C: D.

I could very well have A:B = 1:2 and also C: D = 1:2, but where A = 2, B = 4, C = 3, D = 6. THe ratio stilll holds, but you cannot directly find A:B:C: D unless you have something to compare one of each of the ratios given.
Correct, and I agree.

If A=2B=3C=4D then find
A : B: C: D

Thanks,
Abhijit.

4. Hello, Abhijit!

$\displaystyle \text{Given: }\:A=2B=3C=4D.\;\;\text{Find }\,A : B: C: D$

We have: .$\displaystyle 3C = 4D \quad\Rightarrow\quad C = \tfrac{4}{3}D$

. . $\displaystyle 2B = 3C \quad\Rightarrow\quad B = \tfrac{3}{2}C \quad\Rightarrow\quad B = \tfrac{3}{2}\left(\tfrac{4}{3}D\right)$ . . $\displaystyle \Rightarrow\quad B = 2D$

. . $\displaystyle A = 2B \quad\Rightarrow\quad A = 2(2D) \quad\Rightarrow\quad A = 4D$

$\displaystyle \text{Hence: }\;A:B:C:D \;=\;4D: 2D: \tfrac{4}{3}D: D$

$\displaystyle \text{Multiply by }\tfrac{3}{D}\!:\quad A:B:C:D \;=\;12:6:4:3$

5. Aha!!! Cool..

So you evaluated everything in terms of D and then substituted all the values you derived...

Thanks a lot...

Cheers,
Abhijit.