Question

Ramu is 4 times as old as his son. Five years ago the sum of

their ages was 35 years . Find the son's present age.​

Answer 1

Given

• Ramu is 4 times as old as his son
• 5 Years ago, sum of their ages was 35 years

Explanation

☯ Let the age of the son x be and the age of the Ramu be 4x.

5 Years ago,

• Son's age = (x - 5) Years
• Ramu's Age = (4x - 5)

☯ According to Question,

$\colon\implies{\sf{ (x-5)+(4x-5) = 35 }} \\ \\ \\ \colon\implies{\sf{ x-5+4x-5 = 35 }} \\ \\ \\ \colon\implies{\sf{ 5x-10 = 35 }} \\ \\ \\ \colon\implies{\sf{ 5x = 35 + 10 }} \\ \\ \\ \colon\implies{\sf{ 5x = 45 }} \\ \\ \\ \colon\implies{\sf{ x = \cancel{ \dfrac{45}{5} } }} \\ \\ \\ \colon\mapsto{\sf{ x = 9 }}$

Hence,

• The age of the son = x = 9 Years
• Father's age = 4x = 4×9 = 36 Years

$\\ \maltese \ {\large{\pmb{\underline{\sf{ Verification : }}}}} \\ \\ \\ \colon\mapsto{\sf{ (x-5)+(4x-5) = 35 }} \\ \\ \\ \colon\mapsto{\sf{ (9-5)+(4 \times 9 - 5 ) = 35 }} \\ \\ \\ \colon\mapsto{\sf{ (4)+(36-5)=35 }} \\ \\ \\ \colon\mapsto{\sf{ 4+31 = 35 }} \\ \\ \\ \colon\mapsto{\sf{ 35=35}} \\ \\ \\ \colon\mapsto{\orange{\large{\pmb{\sf{ LHS = RHS }}}}}$