Multiple choice

The average age of $4$ brothers is $9$ years. The age of the eldest of them is double the age of the youngest. The sum of the ages of the middle two brother is $18$ years. Calculate the age of eldest brother .

  1. $14$ years
  2. $12$ years
  3. $15$ years
  4. $11$ years
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B Correct answer
Explanation

Let the ages be a, b, c, d. Sum = 36. d = 2a. b+c = 18. Then a + 2a + 18 = 36, so 3a = 18, a = 6. The eldest is 2a = 12.

AI explanation

The sum of the ages of all 4 brothers is the average multiplied by the number of brothers, which is 9 times 4 = 36 years. Let the youngest brother's age be y, making the eldest brother's age 2y since it is double the youngest. The sum of the middle two brothers is 18, so the equation for the total age is 2y + y + 18 = 36. Solving this gives 3y = 18, so y = 6, and the eldest brother is 2 times 6 = 12 years old.

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