If a : b = 2 : 3 and b : c = 4 : 5 than find a :b c: ​

Question

`if a : b = 2 : 3 and b : c = 4 : 5 than find a :b c:`
​

Answer 1

a:b:c=8:12:15

Explanation:

Combined Ratio

We are given the ratios:

a:b=2:3

b:c=4:5

The combined ratio a:b:c will include all three variables in one single expression.

Before finding it, we must have a common number for the common variable (b). Since b is 3 in the first ratio and 4 in the second ratio, we must equate both by finding the LCM of 3 and 4=12, thus both ratios will be amplified as follows:

a:b=2:3=(2*4):(3*4)=8:12

b:c=4:5=(4*3):(5*3)=12:15

Now there is a common factor in both ratios, we can combine them removing the common factor:

a:b:c=8:12:15