If A:B is 2:3, B:C is 4:5 and C:D is 6:8. Find A:B:C:D

Question

If A:B is 2:3, B:C is 4:5 and C:D is 6:8. Find A:B:C:D?

I am able to find A:C , B:D.

$\frac{A}{C} = \frac{A}{B} × \frac{B}{C}$

$\frac{B}{D} = \frac{B}{C} × \frac{C}{D}$

But I am not able to find A:B:C:D.

I think the difficulty here is largely notational. While $A:B$ is commonly used to denote a ratio of two items (often of lengths without units needed), extending this convention to multiple items is less familiar. — hardmath, Dec 21 '16 at 03:07
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Kanwaljit Singh · Accepted Answer · 2016-12-20T16:46:14.450

0

Given,

$A:B = 2:3$

$A=2x, B=3x$

$B:C = 4:5$

$B=4x, C=5x$

Now in above two ratios in first B has 3x value and in second B has 4x value. Take LCM of 3x, 4x. You have 12x.

To make the value of B in first ratio to 12x . Multiply first ratio with 4x and in other ratio with 3x.

You have,

$A:B = 8x:12x$ and $B:C = 12x:15x$

On combining these two,

$A:B:C = 8x:12x:15x$

Now,

$C:D = 6:8$

$C = 6x, D = 8x$

Now in above two ratios in first C has 15x value and in second C has 6x value. Take LCM of 15x, 6x. You have 30x.

To make the value of C in first ratio to 30x . Multiply first ratio with 2x and in other ratio with 5x.

$A:B:C = 16x:24x:30x$

$C:D = 30x:40x$

On combining these two,

$A:B:C:D = 16x:24x:30x:40x$

If eliminate x.

We have $A:B:C:D = 16:24:30:40$

You can also divide ratio by 2 because all terms have 2 in common.

edited Dec 20 '16 at 16:46

answered Dec 20 '16 at 16:39

Kanwaljit Singh

Sir, everything is clear. But how did you combine the ratios? – Sunny Dec 20 '16 at 16:46
Just think that duplicated value not allowed. – Kanwaljit Singh Dec 20 '16 at 16:47
Like you have A:B:C so on combining with C:D its become A:B:C:C:D. But not to repeat any value so it is A:B:C:D. Similarly for right hand side values. – Kanwaljit Singh Dec 20 '16 at 16:49
I got it. Thank you very very much. – Sunny Dec 20 '16 at 16:50
Mine pleasure. Happy to help you. – Kanwaljit Singh Dec 20 '16 at 16:52
One more thing. Your question is good but you have to edit it to stop down vote responses from others. So in your question write how you are getting A:C and B:D. Then write can't find A:B:C:D. – Kanwaljit Singh Dec 20 '16 at 16:55
Yes .. Thanks for the suggestion. – Sunny Dec 20 '16 at 16:59

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