A, B and C do certain investments for time periods in the

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A, B and C do certain investments for time periods in the ratio of 2 : 1 : 8. At the and of the business term, they received the profits in the ratio of 3 : 4 : 2. Find the ratio of investments of A, B and C.

1. 6 : 16 : 1
2. 2 : 5 : 1
3. 6 : 17 : 1
4. 6 : 19 : 3
5. None of the above

Correct Option: A

Let required ratio of investments be
I₁ : I₂ : I₃.
Ratio of investments = Ratio of profits
2I₁ : I₂ : 8I₃ = 3 : 4 : 2
Taking first two terms of the ratio
(2I₁) / I₂ = 3/4
⇒ I₁ / I₂ = 3/8 = 6/16
⇒ I₁ : I₂ = 6 : 16
Taking last two terms of the ratio ,
I₂ / (8I₃) = 4/2
⇒ I₂/I₃ = 16/1
⇒ I₂ : I₃ = 16 : 1
∴ I₁ : I₂ : I₃ = 6 : 16 : 1