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

Question: If 

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

Answer: 

8:15

Additional Information :

We are given the ratios:

$$a : b = 2 : 3$$ $$b : c = 4 : 5$$

Step 1: Make the Common Term Equal

Since $b$ appears in both ratios, we need to make its values the same.

• In $a : b = 2 : 3$, $b = 3$.
• In $b : c = 4 : 5$, $b = 4$.

To make them equal, we take the LCM of 3 and 4, which is 12.

Now, adjust both ratios:

• Multiply $a : b = 2 : 3$ by 4 → $a : b = 8 : 12$.
• Multiply $b : c = 4 : 5$ by 3 → $b : c = 12 : 15$.

Step 2: Combine the Ratios

Now, we have:

$$a : b : c = 8 : 12 : 15$$

Thus, the ratio $a : c$ is:

$$\mathbf{8 : 15}$$

Final Answer:

$$\boxed{{\displaystyle 8:15}}$$

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