Question

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 of each one of them?

Answer 1

Hint: We need to consider the age of Baichung’s father as x. Baichung is 29 years younger than his father which means Baichung’s age is $x - 29$ and Baichung’s grandfather is 26 years older than Baichung’s father which means Baichung’s grandfather age is $x + 26$. Add the ages of these three people and equate it to 135 then we will get the ages of these 3 people.


Complete step-by-step Solution:
We are given that 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.
We have to find the age of each one of them.
Let us consider the age of Baichung’s father as ‘x’.
Baichung is 29 years younger than his father. So, his age becomes $x - 29$
Baichung’s grandfather is 26 years older than Baichung’s father. So, Baichung’s grandfather age become $x + 26$
The sum of the ages of all the three is 135 years which means
$
  x + \left( {x + 26} \right) + \left( {x - 29} \right) = 135 \\
  3x + 26 - 29 = 135 \\
  3x - 3 = 135 \\
  3x = 135 + 3 \\
  3x = 138 \\
  x = \dfrac{{138}}{3} \\
  x = 46 \\
 $
Therefore, the age of Baichung’s father is x=46 years.
Age of Baichung is $x - 29 \to 46 - 29 = 17$ years.
Age of Baichung’s Grandfather is $x + 26 \to 46 + 26 = 72$ years.


Note: Another approach to the above problem
Consider Baichung’s Age as ‘x’, then his father age becomes $x + 29$ and his grandfather’s age becomes $x + 29 + 26$
$
  x + x + 29 + x + 29 + 26 = 135 \\
  3x + 84 = 135 \\
  3x = 135 - 84 \\
  3x = 51 \\
  x = \dfrac{{51}}{3} = 17 \\
 $
Age of Baichung is 17 years.
Age of Baichung’s father is $x + 29 \to 17 + 29 = 46$ years.
Age of Baichung’s Grandfather is $x + 29 + 26 \to 17 + 29 + 26 = 72$ years.