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If (x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c, then find a ∶ b ∶ c.
  • a)
    23 ∶ 21 ∶ 22
  • b)
    23 ∶ 22 ∶ 21
  • c)
    21 ∶ 22 ∶ 23
  • d)
    22 ∶ 23 ∶ 21
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If (x – a) (x – b) (x – c) = 10 11 12 and 2x = a...
(x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c,
⇒ (x – a) = (a + b + c) /2 – a = (b + c – a) /2 = 10      ---- 1
⇒ (x – b) = (a + b + c) /2 – b = (a + c – b) /2 = 11      ---- 2
⇒ (x – c) = (a + b + c) /2 – c = (a + b – c) /2 = 12      ---- 3
From equation 2 and 3,
⇒ (a + c – b) = 22
⇒ (a + b – c) = 24
⇒ a = 23
Similarly, b = 22 and c = 21
∴ a ∶ b ∶ c = 23 ∶ 22 ∶ 21
Most Upvoted Answer
If (x – a) (x – b) (x – c) = 10 11 12 and 2x = a...
(x – a) ∶ (x – b) ∶ (x – c) = 10 ∶ 11 ∶ 12 and 2x = a + b + c,
⇒ (x – a) = (a + b + c) /2 – a = (b + c – a) /2 = 10      ---- 1
⇒ (x – b) = (a + b + c) /2 – b = (a + c – b) /2 = 11      ---- 2
⇒ (x – c) = (a + b + c) /2 – c = (a + b – c) /2 = 12      ---- 3
From equation 2 and 3,
⇒ (a + c – b) = 22
⇒ (a + b – c) = 24
⇒ a = 23
Similarly, b = 22 and c = 21
∴ a ∶ b ∶ c = 23 ∶ 22 ∶ 21
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