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.

Comments