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Given that,

  • $a:b=3:4$
  • $b:c=2:1$

We can combine the ratios,

  • $a:b=(3:4)\times 2 = 6:8$
  • $b:c=(2:1)\times 4 = 8:4$

 $\Rightarrow a:b:c =6:8:4=3:4:2$

Let   $a=3k,b=4k,c=2k$

$\therefore$ The value of $a+b+c = 3k+4k+2k= 9k$  

The number $207$ is divisible by $9$. We can write $207 = 9 \cdot 23.$

$\textbf{PS:}\; \textsf{Divisibility by 9:-}$ The sum of digits of the number must be divisible by $9.$

Correct Answer $:\text{C}$

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