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?​

Answer 1

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Given Information :

• Baichung’s father is 26 years younger than Baichung’s grandfather.

• Baichung’s father is 29 years older than Baichung.

• The sum of the ages of all the three is 135 years.

To calculate :

• What is the age of each one of them?

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Clarification :

Here, we are given that Baichung’s father is 26 years younger than Baichung’s grandfather and 29 years older than Baichung and the sum of the ages of all the three is 135 years.

We'll first assume Baichung’s father's age as a variable, say x years. After that, we'll make the expressions of the ages of Baichung’s grandfather and Baichung in the terms of Baichung’s father's age. After that, by forming a linear equation and solving that equation, we'll find the age of each one of them.

So, let's commence the steps!

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Explication of steps :

Let us assume Baichung’s father's age as x years.

• Baichung's father's age ⇒ x years

★ According to the question,

⇒ Baichung’s father is 26 years younger than Baichung’s grandfather._(1)

⇒ Baichung's father's age = Age of Baichung's grandfather – 26

⇒ x = Age of Baichung's grandfather – 26

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

Also,

⇒ Baichung’s father is 29 years older than Baichung._(2)

⇒ Baichung's father's age = Age of Baichung + 29

⇒ x = Age of Baichung + 29

⇒ Age of Baichung = (x – 29) years

As per the provided question,

➝ The sum of the ages of all the three is 135 years._(3)

➝ Baichung's father's age + Baichung's grandfather's age + Baichung's age = 135

➝ x + (x + 26) + (x – 29) = 135

➝ x + x + 26 + x – 29 = 135

➝ 3x – 3 = 135

➝ 3x = 135 + 3

➝ 3x = 138

➝ x = $\sf { \cancel { \dfrac{138}{3} } }$

➝ x = 46

Therefore,

⇒ Baichung's father's age = x years

⇒ Baichung's father's age = 46 years

And,

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

⇒ Age of Baichung's grandfather = (46 + 26) years

⇒ Age of Baichung's grandfather = 72 years

Also,

⇒ Age of Baichung = (x – 29) years

⇒ Age of Baichung = (46 – 29) years

⇒ Age of Baichung = 17 years

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Answer 2

Answer:

Given :

Baichung 's father is 26 years younger than Baichung's grandfather and 29 year older than Baichung .

The sum of the age of all the three is 135 years.

Solution :

$\longmapsto\tt{Let\:Age\:of\:Grandfather\:be=x}$

As Given that Baichung 's father is 26 years younger than Baichung's grandfather and 29 year older than Baichung .So ,

$\longmapsto\tt{Age\:of\:Baichung's\:Father=x-26}$

$\longmapsto\tt{Age\:of\:Baichung=x-26-29=x-55}$

A.T.Q :

$\longmapsto\tt{x+x-26+x-55=135}$

$\longmapsto\tt{3x-81=135}$

$\longmapsto\tt{3x=135+81}$

$\longmapsto\tt{3x=216}$

$\longmapsto\tt{x=\cancel\dfrac{216}{3}}$

$\longmapsto\tt\bf{x=72}$

Value of x is 72 .

Therefore :

$\longmapsto\tt{Age\:of\:his\:Grandfather=x}$

$\longmapsto\tt\bf{72\:yrs}$

$\longmapsto\tt{Age\:of\:his\:Father=72-26}$

$\longmapsto\tt\bf{46\:yrs}$

$\longmapsto\tt{Age\:of\:Baichung=72-55}$

$\longmapsto\tt\bf{17\:yrs}$