Baichung's dather 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?

Grandfather: X years old.

Father: x-26 years old.
Son: (x-26)-29 = x-55.

x + x-26 + x-55 = 135, 3x - 81 = 135, 3x = 216, X = 72, x-26 = 46, x-55 = 17.

To solve this problem, let's represent the age of Baichung as B, the age of Baichung's father as F, and the age of Baichung's grandfather as G.

From the information provided, we know that:
1. Baichung's father is 26 years younger than Baichung's grandfather: F = G - 26
2. Baichung's father is 29 years older than Baichung: F = B + 29
3. The sum of the ages of all three is 135 years: B + F + G = 135

Now, we can solve this system of equations to find the ages of each person.

Substituting the values from equation 1 into equation 2, we get:
G - 26 = B + 29 --> G = B + 55

Substituting the values from equations 1 and 3 into equation 2, we get:
B + 55 + B - 26 = 135 --> 2B + 29 = 135 --> 2B = 106 --> B = 53

Now that we know B = 53, we can substitute this value into equation 2 to find F:
F = B + 29 = 53 + 29 = 82

Finally, we can find G by substituting B = 53 into G = B + 55:
G = 53 + 55 = 108

Therefore, the ages of each person are:
Baichung is 53 years old,
Baichung's father is 82 years old,
and Baichung's grandfather is 108 years old.