Question

Baichung’s father's age 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?

Answer 1

Hint: Here Baichung’s age is unknown and from this unknown value we can find other two person’s age and also we know that to find the value of one unknown value we need only one equation for determining the value of that unknown and here the unknown value is Baichung’s age and the equation is the equation of the sum of the ages of all the three persons. So by equating we can find the answers.

Complete step by step answer:
Step 1: let the age of Baichung be ‘x’
And according to the question, Baichung’s father is 29 years older than Baichung. Therefore, we have
Baichung’s father age \[ = x + 29\] years
Also, according to the question, Baichung’s father age is 26 years younger than Baichung’s grandfather, therefore we have
Baichung’s grandfather age \[ = x + 29 + 26\]
Step 2: Now, according to the question the sum of the ages of all three is 135 years. Therefore, we can write this as
Baichung’s age + Baichung’s father age + Baichung’s grandfather age \[ = 135\]
\[ \Rightarrow \] \[x + x + 29 + x + 29 + 26 = 135\]
Adding all the terms, we get
\[3x + 84 = 135\]
\[ \Rightarrow \] \[3x = 135 - 84\]
\[ \Rightarrow \] \[3x = 51\]
Taking 3 on the right-hand side in the denominator, we get
\[x = \dfrac{{51}}{3}\]
Further simplifying
\[x = 17\]
Step 3: determining ages of all the three
Initially, we have let that Baichung’s age is ‘x’, and \[x = 17\]
Therefore,
Baichung’s age \[ = 17\] years
Also, we have,
Baichung’s father age \[ = x + 29\] years
Substituting the value of ‘x’ above, we get
Baichung’s father age \[ = 17 + 29 = 46\] years
And, Baichung’s grandfather age \[ = x + 29 + 26\]
Substituting the value of ‘x’ above, we get
Baichung’s grandfather age \[ = 17 + 29 + 26 = 72\] years

Note: First, generate the required equation and place the values of unknown correctly in the equation then solve the equation to find the answer.
For ‘n’ number of unknowns generate ‘n’ number of equations and then solve that equation to get values of unknown.