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.

Answer 1

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.