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If (a + b + c) ∶ d = 5 ∶ 1, (b + c + d) ∶ a = 7 ∶ 1 and, (c + d + a) ∶ b = 3 ∶ 1 then find a ∶ b ∶ c ∶ d.1. 1 ∶ 2 ∶ 3 ∶ 42. 3 3. 2 ∶ 4 ∶ 9 ∶ 64. 3 ∶ 9 ∶ 6 ∶ 5 |
| Answer» Correct Answer - Option 2 : 3 Given:(a + b + c) ∶ d = 5 ∶ 1(b + c + d) ∶ a = 7 ∶ 1(c + d + a) ∶ b = 3 ∶ 1Calculations:(a + b + c) ∶ d = 5 ∶ 1Let ‘a + b + c’ be ‘5x’ and ‘d’ be ‘x’So, a + b + c + d = 5x + x = 6x (b + c + d) ∶ a = 7 ∶ 1⇒ (a + b + c + d)/a = (1 + 7)/1 = 8/1So, a = (6x/8) × 1 = 3x/4 (c + d + a) ∶ b = 3 ∶ 1⇒ (a + b + c + d)/b = (1 + 3)/1 = 4/1So, b = (6x/4) = 3x/2 Now, c = (a + b + c + d) – (a + b + d)⇒ 6x – ((3x/4) + (3x/2) + (x))⇒ 6x – (3x + 6x + 4x)/4⇒ 6x – 13x/4 = 11x/4 So, a ∶ b ∶ c ∶ d = (3x/4) ∶ (3x/2) ∶ (11x/4) ∶ x ⇒ 3x ∶ 3x × 2 ∶ 11x ∶ 4 × x⇒ 3 ∶ 6 ∶ 11 ∶ 4 ∴ The value of a ∶ b ∶ c ∶ d is 3 ∶ 6 ∶ 11 ∶ 4 | |