Question

11. 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 1

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The age of Baichung is 17 years

The age of Baichung's father is 46 years.

And the age Baichung's Grandfather is 72 years.

Solution:-

Let the age of Baichung's father be x

As it is given, Baichung's father is 26 years than younger Baichung's grandfather and 29 years older than Baichung, Therefore:-

Age of Baichung's Grandfather = (x + 26) years

And age of Baichung = (x - 29) years

Sum of their ages is = 135

According to the question,

=> x + (x + 26) + (x - 29) = 135

=> x + x + 26 + x - 29 = 135

=> 3x + 26 - 29 = 135

=> 3x - 3 = 135

=> 3x = 135 + 3

=> 3x = 138

=> x = 138/3

=> x = 46

Hence the age of Baichung Father is 46.

Now, the age of Baichung => (46 - 29) = 17 years

And the age of Baichung's Grandfather => (46 + 26) = 72 years

Answer 2

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Let the age of Baichung’s father = m year

Since, Baichung’s father is 26 year younger than Baichung’s grand father

Therefore, Age of Baichung’s grandfather = Age of Baichung’s father + 26 = m + 26 year

Since, Baichung’s father is 29 year older than Baichung

Therefore, Age of Baichung = Age of Baichung’s father – 29 = m – 29 year

Now, we have

Age of Baichung = m – 29 year

Age of Baichung’s father = m year

Age of Bahichung’s grandfather = m + 26 year

According to question, the sum of ages of all the three = 135 year

Therefore,

• Age of Baichung + Age of Baichung’s father + Age of Baichung’s grandfather = 135

⇒ (m – 29) + m + (m + 26) = 135 year

⇒ m – 29 + m + m + 26 = 135 year

⇒ m + m + m – 29 + 26 = 135 year

⇒ 3m – 3 = 135 year

After transposing – 3 to the RHS, we get

3m = 135 year + 3

⇒ 3m = 138 year

After dividing both sides by 3, we get

• This means age of Baichung’s father = 46 year

Now, by substituting the value of m, we can calculate the age of Baichung and the age of Baichun’s grandfather.

Therefore,

Age of Baichung = m – 29 = 46 – 29 = 17 year

Age of Baichung’s grandfather = m + 26 = 46 + 26 = 72 year

Thus,

• Age of Baichung = 17 year

• Age of Baichung’s father = 46 year

• Age of Baichung’s grandfather = 72 year

Hope it helps you!

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