Multiple choice

Baichung's father is $26$ years younger than Baichung's grandfather and $29$ years older than Baichung. The sum of the ages of all the three is $135$ years. What is the age of each one of them?

  1. Baichung's age is $12$ years, his father's age is $35$ years and his grandfather's age is $65$.
  2. Baichung's age is $18$ years, his father's age is $45$ years and his grandfather's age is $66$.
  3. Baichung's age is $26$years, his father's age is $55$ years and his grandfather's age is $84$.
  4. Baichung's age is $17$ years, his father's age is $46$ years and his grandfather's age is $72$.
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D Correct answer
Explanation

Let Baichung's age be x. His father is x+29 and his grandfather is (x+29)+26 = x+55. The sum x + (x+29) + (x+55) = 135 simplifies to 3x + 84 = 135, so 3x = 51, meaning x = 17. Thus, Baichung is 17, his father is 46, and his grandfather is 72.

AI explanation

Let Baichung's present age be x, his father's age be x + 29, and his grandfather's age be (x + 29) + 26 = x + 55. The sum of their ages is 135, giving the equation x + (x + 29) + (x + 55) = 135. Combining terms results in 3x + 84 = 135, so 3x = 51, meaning Baichung is 17 years old. Consequently, his father is 17 + 29 = 46 years old, and his grandfather is 46 + 26 = 72 years old.

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