# If a : b : c = 2 : 3 : 4 and 2a – 3b + 4c = 33, then the value of c is :

If a : b : c = 2 : 3 : 4 and 2a – 3b + 4c = 33, then the value of c is :
[A]$6$
[B]$9$
[C]$12$
[D]$\frac{66}{7}$

$\mathbf{12}$
$a : b : c = 2 : 3 : 4$
$\therefore \frac{a}{2} = \frac{b}{3} = \frac{c}{4} = k (let)$
$=> a = 2k, b = 3k, c = 4k$
Given, $2a - 3b + 4c = 33$
$=> 2\times 2k - 3\times 3k + 4\times 4k = 33$
$=> 4k - 9k + 16k = 33$
$=> 11k = 33$
$=> k = \frac{33}{11} = 3$
$\therefore c = 4k = 4\times 3 = 12$
Hence option [C] is correct answer.