If a : b = 3 : 2 and b : c = 3 : 2, then a : b : c = ?

Correct option is A

Given:

two ratios:

a : b = 3 : 2

b : c = 3 : 2

To find the combined ratio a : b : c.

Solution: 

From a : b = 3 : 2,

let a = 3x and b =2x, where x is some constant.
From b : c = 3 : 2,

let b = 3y and c = 2y, where y is some constant.

Since both equations contain $b$,

2x = 3y

$$x = \frac{3}{2}y$$ 

Now substitute $$x = \frac{3}{2}y$$​ into the expressions for a, b, and c:

​$$a = 3x = 3 \times \frac{3}{2}y = \frac{9}{2}y,$$ 

$$b = 2x = 2 \times \frac{3}{2}y = 3y$$ ​​

$$c = 2y$$ 

​Thus, the combined ratio is:

​$$a : b : c = \frac{9}{2}y : 3y : 2y$$ 

a: b : c = $$\frac{9}{2}$$​ : 3 : 2. 

a : b : c =  9 : 6 : 4 

​Thus the combined ratio $a:b:c$ is: $$9:6:4$$ . 

Alternate Solution: 

a : b = 3 : 2.......(1)

b : c = 3 : 2 .......(2) 

b is common in both so multiplying by 3 in (1) and multiplying by 2 in (2) 

So, a : b : c = 9 : 6 : 4