Question

A father said to his son I was twice as old as you are at present at time of your birth. If the father's age is 48 years now then the son's age 5 years back was

Answer 1

$\huge{\underline{\purple{\rm{Question:}}}}$

A father said to his son I was twice as old as you are at present at time of your birth. If the father's age is 48 years now then the son's age 5 years back was.

$\huge{\underline{\purple{\rm{Solution:}}}}$

$\large{\underline{\red{\rm{Let:}}}}$

• $\rm{The\: present\:age\:of\:man=48\: year's}$
• $\rm{The\: present\:age\:of\:son=y\: year's}$
• $\rm{The\:age\:of\:son\:5\: years\:ago=y-5\:year's}$

$\large{\underline{\red{\rm{To\: Find:}}}}$

• $\sf{The\:son's\:age\:5\: year's\:ago}$

$\small{\underline{\green{\rm{According to\:the\: Question:}}}}$

$\sf{The\:man\:was\: twice\:as\:old\:as\:his\:son\:at\:his\:birth}$

$\sf{\implies 48=2y}$

$\sf\purple{\implies y=24}$

Hence,

$\sf{\implies 5\: year's\: ago\:the\:age\:of\:son=y-5}$

$\sf{\implies 5\: year's\: ago\:the\:age\:of\:son=24-5}$

$\sf\purple{\implies 5\: year's\: ago\:the\:age\:of\:son=19\: year's}$

Answer 2

Let the son's age be y.

Given

The Father's age = 48 years

According to the question

$2y=48$

$\implies y = \dfrac{48}{2}$

$\implies y =24$

Therefore, the son's age at present is 24 years.

Let the son's age 5 years back be y - 5.

$\implies y - 5\\\implies 24-5\\\implies 19 \ years$

$\boxed{\boxed{\bold{Therefore, \ the \ son's \ age \ 5 \ years \ ago \ was \ 19 \ years}}}}}$