1.

If (a + b + c) ∶ d = 3 ∶ 1, (b + c + d) ∶ a = 5 ∶ 1 and, (c + d + a) ∶ b = 2 ∶ 1 then find a ∶ b ∶ c ∶ d. 1. 7 ∶ 2 ∶ 3 ∶ 42. 2 ∶ 4 ∶ 3 ∶ 33. 5 ∶ 4 ∶ 9 ∶ 64. 3 ∶ 9 ∶ 6 ∶ 5

Answer» Correct Answer - Option 2 : 2 ∶ 4 ∶ 3 ∶ 3

Given:

(a + b + c) ∶ d = 3 ∶ 1

(b + c + d) ∶ a = 5

(c + d + a) ∶ b = 2 ∶ 1

Calculations:

Let a + b + c + d be x

(a + b + c) ∶ d = 3 ∶ 1

Now, d = (x/4) × 1 = x/4

(b + c + d) ∶ a = 5 ∶ 1

Now, a = (x/6) × 1 = x/6

(c + d + a) ∶ b = 2 ∶ 1

Now, b = (x/3) × 1 = x/3

c = (a + b + c + d) – (a + b + d)

⇒ x – ((x/4) + (x/6) + (x/3))

⇒ x – (6x + 4x + 8x)/24

⇒ (24x – 18x)/24

⇒ x/4

So a ∶ b ∶ c ∶ d = x/6 ∶ x/3 ∶ x/4 ∶ x/4

⇒ a ∶ b ∶ c ∶ d = 2 ∶ 4 ∶ 3 ∶ 3

∴ a ∶ b ∶ c ∶ d is 2 ∶ 4 ∶ 3 ∶ 3


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