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# 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?

Last updated date: 13th Jun 2024
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Answer
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Hint: In this question, we have the conditions between the ages of three persons. Also, the sum of their ages is given.
We need to first take the age of anyone as a random variable. Then applying the conditions we will get the other two ages. Then apply them in the other condition we can find the value of the random variable. Then we can easily find out the required solution.

Complete step by step answer:
It is given that Baichung's father is $26$ years younger than Baichung’s grandfather and $29$ years older than Baichung.
Also given that, the sum of the ages of all the three is $135$ years.
We need to find out the age of each one of them.
Let, the age of Baichung’s father is $x$ years.
Then the age of Baichung’s grandfather is $= x + 26$ years.
The age of Baichung is $= x - 29$ years.
Then the sum of all three of them is $= x + x + 26 + x - 29$
Thus we get,
$\Rightarrow x + x + 26 + x - 29 = 135$
Simplifying we get,
$\Rightarrow 3x - 3 = 135$
Arranging the constant terms on the same side,
$\Rightarrow 3x = 135 + 3$
Adding the terms we get,
$\Rightarrow 3x = 138$
Solving for $x$ we get,
$\Rightarrow x = \dfrac{{138}}{3}$
Hence the value of $x$ is,
$\Rightarrow x = 46$ years
Since $x$ the age of Baichung’s father
The age of Baichung’s father is $46$ years.
Then the age of Baichung’s grandfather is $46 + 26 = 72$ years.

$\therefore$ The age of Baichung is $46 - 29 = 17$ years.

Note:
Like this finding age problem we have to be careful on substituting the values of given. Because students may get mistaken in solutions. So we must concentrate on that calculation. The linear equations in one variable is an equation which is expressed in the form of $ax + b = 0$ , where $a$ and $b$ are two integers and $x$ is a variable and has only one solution. For example, $2x + 8 = 4$ is a linear equation having a single variable in it. Therefore, this equation has only one solution, which is $2x = 4 - 8 = - 4$. That is, $x = \dfrac{{ - 4}}{2} = - 2$.