question_answer 12)

                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?         

Answer:

                            Let the age of Baichung be\[x\] years. Then, the age of Baichung's father \[=(x+29)\]years and,       the age of Baichung's grandfather \[=(x+29+26)\]years \[=(x+55)\]years \[\because \]     The sum of the ages of all three is 135 years. \[\therefore \]  \[x+(x+29)+(x+55)=135\] \[\Rightarrow \]               \[3x+84=135\] \[\Rightarrow \]               \[3x=135-84\]                    | Transposing 84 to RHS \[\Rightarrow \]               \[3x=51\] \[\Rightarrow \]               \[x=\frac{51}{3}\,=17\]                 | Dividing both sides by 3 \[\Rightarrow \]               \[x+29=17+29=46\] and,       \[x+55=17+55=72\] Hence, the ages of Baichung, Baichung's father and Baichung's grandfather are 17 years, 46 years and 72 years respectively. Check: \[46=17+29\]                 \[72=46+26\]     | as desired \[17+46+72=135\].