Question

the age of rahul is 4 years more than 4 times of anish' sage. the age of anu is the sum of anish's age and one fourth of rahul's age. the sum of all their ages is 89 years. find theri ages

Answer 1

Appropriate Question:

The age of Rahul is 4 years more than 4 times of Anish's age. The age of Anu is the sum of Anish's age and one fourth of Rahul's age. The sum of all their ages is 89 years. Find their ages.

Required Solution:

Given :

• Age of Rahul = 4 years more than 4 times of Anish's age

• Age of Anu = The sum of Anish's age and one fourth of Rahul's age

• Sum of all their ages = 89 years.

To calculate :

• Their ages i.e, age of Rahul, Anish & Anu

Calculations :

Let,

• Age of Anish be "x".

➨ Age of Anish = x years

According to the question :

➨ Age of Rahul = ( 4 + 4x ) years

[ Since, age of Rahul is 4 years more than 4 times of Anish's age.]

➨ Age of Anu = x + $\bf{ \dfrac{1}{4} }$ × ( 4 + 4x )

[ Since, age of Anu is the sum of Anish's age and one fourth of Rahul's age. ]

➳ Age of Anu = $\sf { x + \dfrac{1}{\not{4}} (\not{4}) + \dfrac{1}{4} (4x) }$

➳ Age of Anu = $\sf {x + 1 + \dfrac{\not{4}x}{\not{4}}}$

➳ Age of Anu = $\sf { x + 1 + x }$

➳ Age of Anu = 2x + 1

Also,

➨ Age of Anish + Age of Rahul + Age of Anu = 89

➨ x + ( 4 + 4x ) + ( 2x + 1 ) = 89

➨ x + 4 + 4x + 2x + 1 = 89

➨ 7x + 5 = 89

➨ 7x = 89 - 5

➨ 7x = 84

➨ x = $\sf { \dfrac{84}{7} }$

➨ x = 12

Henceforth,

➤ Age of Anish = x years

➤ $\underline { \bf \purple{ Age \: of \: Anish = 12 \: years}}$

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➤ Age of Rahul = ( 4 + 4x ) years

➤ Age of Rahul = [ 4 + 4(12) ] years

➤ Age of Rahul = ( 4 + 48 ) years

➤ $\underline { \bf \purple{ Age \: of \: Rahul = 52 \: years}}$

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➤ Age of Anu = ( 2x + 1 ) years

➤ Age of Anu = [ 2(12) + 1 ] years

➤ Age of Anu = ( 24 + 1 ) years

➤ $\underline { \bf \purple{ Age \: of \: Anu = 25 \: years}}$