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Mathematics

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

  1. 6

  2. 9

  3. 667\dfrac{66}{7}

  4. 12

Ratio Proportion

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Answer

Given,

a : b : c = 2 : 3 : 4

Let a = 2k, b = 3k and c = 4k for some constant k.

Substituting value of a, b and c in 2a − 3b + 4c = 33, we get :

⇒ 2(2k) − 3(3k) + 4(4k) = 33

⇒ 4k - 9k + 16k = 33

⇒ 11k = 33

⇒ k = 3311\dfrac{33}{11}

⇒ k = 3.

⇒ 4k = 4(3) = 12.

Hence, option 4 is the correct option.

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