Question

Ronav's mother is 20 years older than him. After five
years, she will be thrice Ronav's age. What are their
ages now?
​

Answer 1

Given :

• Ronav's mother is 20 years older than him.
• Five years later, she will be thrice Ronav's age.

To find :

• The present age of Ronav and his mother.

Solution :

Let,

• Present age of Ronav = x years
• Present age of Ronav's mother = x + 20 years

Their ages after 5 years,

Add 5 years in the ages of Ronav and his mother.

• Ronav's age after 5 years = x + 5 years
• Ronav's mother's age after 5 years= x + 20 + 5 = x + 25 years

According to the question,

→ x + 25 = 3(x + 5)

→ x + 25 = 3x + 15

→ x - 3x = 15 - 25

→ - 2x = - 10

→ 2x = 10

→ Transposing 2 to the other side.

→ x = 10 ÷ 2

→ x = 5

The value of x = 5.

Substitute the value of x in the ages of Ronav and his mother.

→ Ronav's present age = x = 5 years

→ Ronav's mother's present age = x + 20 = 5 + 20 = 25 years

Answer 2

Let the present age of the Ronav be x and his mother's age be (x + 20) years.

After 5 years,

• Ronav's age = (x + 5)
• Mother's age = (x + 20 + 5)

$\maltese \ {\pmb{\underline{\sf{ According \ to \ Question: }}}} \\ \\ \colon\implies{\sf{ 3(x+5) = (x+20+5) }} \\ \\ \\ \colon\implies{\sf{ 3x+15 = x+25 }} \\ \\ \\ \colon\implies{\sf{ 3x-x = 25-15 }} \\ \\ \\ \colon\implies{\sf{ \cancel{2} x = \cancel{10} }} \\ \\ \\ \colon\implies{\sf{ x = 5 }}$

Hence,

• Present age of Ronav = x = 5 years
• Present age of Mother = (x + 20) = (5 + 20) = 25 Years.

$\\ \maltese \ {\large{\pmb{\underline{\underline{\sf{ Verification : }}}}}} \\ \\ \colon\mapsto{\sf{ 3(x+5) = (x+20+5) }} \\ \\ \colon\mapsto{\sf{ 3(5+5) = (5+20+5) }} \\ \\ \colon\mapsto{\sf{ 3(10) = (30) }} \\ \\ \colon\mapsto{\sf{ 30 = 30 }} \\ \\ \colon\mapsto{\underline{\underline{\sf\red{ LHS = RHS }}}}$