Number Theory/Ratio

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Question
If A:B = 2:3 , B:C = 4:5 , C:D = 6:7. Find A:B:C:D.
Please answer it quickly sir

Answer
If we look at A:B and B:C, we see in the 1st, B is 3 and in the 2nd, B is 4.
These both divide evenly into 12, so change both to make B 12.

For A:B, since 3*4 = 12, we can take 2*4 and get 8, giving A:B as 8:12.
For B:C, since 4*3 = 12, we can take 5*3 and get 15, which gives B:C as 12:15.
Thus, A:B:C is 8:12:15.

Now if we look at the numbers used for C, they are 15 and 6.
The smallest number that is divisible by 15 and 6 is 30.

This means that 8:12:15 needs to be  multiplied by 30/15 = 2, giving 16:24:30.
This means that since 30/6 = 5, multiply the C:D ratio by 5 and get 30:35.

We can now combine the final answer into the group we have so far since they both have a 30 for C.  This gives A:B:C:D as 16:24:30:35.  

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