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 one of them?

• A. Baichung's age is $12$ years, his father's age is $35$ years and his grandfather's age is $65$.
• B. Baichung's age is $18$ years, his father's age is $45$ years and his grandfather's age is $66$.
• C. Baichung's age is $26$years, his father's age is $55$ years and his grandfather's age is $84$.
• D. Baichung's age is $17$ years, his father's age is $46$ years and his grandfather's age is $72$.

Answer 1

The correct option is D Baichung's age is $17$ years, his father's age is $46$ years and his grandfather's age is $72$.

Let Baichung's age be $x$ years. Then, Baichung's father's age $=(x+29)$ years
Baichung's grandfather's age $=\left[\right(x+29)+26)$ years $=(x+55)$ years
According to the given condition, we have
$x+(x+29)+(x+55)=135$
$\Rightarrow 3x+84=135$
$\Rightarrow 3x=135-84$
$\Rightarrow 3x=51$
$\Rightarrow x=\frac{51}{3}=17$
$\therefore$ Baichung's age is $17$ years, his father's age is $17+29=46$ years and his grandfather's age is $46+26=72$ years.