If a : b = 2 : 5 and b : c = 3 : 4, then find the ratio a : b : c.

The correct answer is 6 : 15 : 20.

Step 1: Identify the given ratios

We are given the following two ratios:

$a:b=2:5$

$b:c=3:4$

Step 2: Make the common term equal

The variable $b$ is present in both ratios. In the first ratio, the term corresponding to $b$ is 5, while in the second ratio, it is 3.

To combine the two ratios into $a:b:c$, we need to make the value of $b$ equal in both ratios by finding the Least Common Multiple (LCM) of 5 and 3, which is 15.

Step 3: Scale each ratio

Multiply the terms of the first ratio $a:b$ by 3:

$a:b=(2\times 3):(5\times 3)=6:15$

Multiply the terms of the second ratio $b:c$ by 5:

$b:c=(3\times 5):(4\times 5)=15:20$

Step 4: Combine into a single ratio

Since $b$ is now 15 in both ratios, we can combine them directly:

$a:b:c=6:15:20$