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Mathematics

If 3A = 5B and 4B = 6C, then A : C is equal to :

  1. 2 : 5

  2. 3 : 5

  3. 4 : 5

  4. 5 : 2

Ratio Proportion

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Answer

Given,

3A = 5B

⇒AB=53\Rightarrow \dfrac{A}{B} = \dfrac{5}{3} ….(1)

Also, 4B = 6C

⇒BC=64=32\Rightarrow \dfrac{B}{C} = \dfrac{6}{4} = \dfrac{3}{2} ….(2)

From (1) and (2):

⇒AC=AB×BC⇒AC=53×32⇒AC=52.\Rightarrow \dfrac{A}{C} = \dfrac{A}{B} \times \dfrac{B}{C} \\[1em] \Rightarrow \dfrac{A}{C} = \dfrac{5}{3} \times \dfrac{3}{2} \\[1em] \Rightarrow \dfrac{A}{C} = \dfrac{5}{2}.

Therefore, A : C = 5 : 2.

Hence, option 4 is the correct option.

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