Continued Ratio

We saw how to handle ratios of different things. But there may be cases where we need to compare two different ratios where one item is common.

For example:

$A:B = 3:4$ and $B:C = 6:7$. Their sum is $105$. How much is $C$?

We can see that in the two given ratios $B$ is common. So we will need to convert the ratios into values where $B$ has the same value.

The $LCM$ of $4$ and $6$ is $12$

Therefore, we can write:

$A:B = 3:4 = 9:12$, and

$B:C = 6:7 = 12:14$

Now we can say that:

$A:B:C = 9:12:14$

We can assume:

$A = 9x$

$B = 12x$

$C = 14x$

$\texttip{\therefore}{therefore} A + B + C = 9x + 12x + 14x = 35x$

$\texttip{\Rightarrow}{follows that} 35x = 105$

$\texttip{\Rightarrow}{follows that} x = \dfrac{105}{35} = 3$

$\texttip{\therefore}{therefore} C = 14x = 14 \times 3 = 42$