Question

A father is 4 times as old as his son now. After 5 years, the father's age will be 3 times his son's age. What are their present ages?​

Answer 1

Given : A father is 4 times as old as his son and After 5 years, the father's age will be 3 times his son's age.

Need To Find : Present age of Father and Son ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

❍ Let's say that , Son's age be x yrs & Father's age be 4x yrs i.e, Father is 4 times as old as his son .

⠀⠀⠀⠀⠀⠀☯︎ After 5 years their Ages :

• Son's age will be : ( x + 5 ) yrs &
• Father's age will be : ( 4x + 5 ) yrs .

$\\\qquad \:\:\:\:\bigstar \:\underline {\pmb{\sf{\red{ According \:To \:The\:Given \:Question \:\::\:}}}}$

⠀▪︎⠀ After 5 years, the father's age will be 3 times his son's age.

$\\\\ \twoheadrightarrow \sf \Big\{ Father's \:Age\:_{\:(After \:5\:Years )\:}\:\Big\}\:=\:3\:\Big\{ Son's \:Age\:_{\:(After \:5\:Years )\:}\:\Big\}\:\:\\\\\\ \twoheadrightarrow \sf \Big\{ 4x + 5\:\Big\}\:=\:3\:\Big\{ x + 5\:\Big\}\:\:\\\\\\\twoheadrightarrow \sf \Big\{ 4x + 5\:\Big\}\:=\:\Big\{ 3x + 15\:\Big\}\:\:\\\\\\ \twoheadrightarrow \sf 4x + 5\:\:\:=\: 3x + 15\:\:\\\\\\\twoheadrightarrow \sf 4x - 3x\:\:\:=\: 15 - 10 \:\:\\\\\\ \twoheadrightarrow \pmb {\underline {\boxed {\purple {\:\frak{ \:x\:\:=\:10\:yrs\:}}}}}\:\bigstar \:$

Therefore,

• Son's age , x = 10 yrs &
• Father's age , 4x = 4(10) = 40 yrs

$\therefore \underline {\sf \: Hence, \:Present \:ages \:of \: Father\:and\:Son \:are\:\pmb{\sf 10\:yrs\:\&\:40\:yrs\:}\:,\:respectively \:.}$

Answer 2

$\huge\purple{ \underline{ \boxed{\mathbb{\red{QUESTION : }}}}}$

A father is 4 times as old as his son now. After 5 years, the father's age will be 3 times his son's age. What are their present ages ?

$\huge\purple{ \underline{ \boxed{\mathbb{\red{ANSWER : }}}}}$

Present age of son = 10 years

Present age of father = 40 years

$\huge\purple{ \underline{ \boxed{\mathbb{\red{EXPLANATION : }}}}}$

$\green{ \large \underline{ \mathbb{\underline{GIVEN : }}}}$

• A father is 4 times as old as his son now.

• After 5 years, the father's age will be 3 times his son's age.

$\green{ \large \underline{ \mathbb{\underline{TO \: FIND : }}}}$

• Their present ages .

$\green{ \large \underline{ \mathbb{\underline{SOLUTION: }}}}$

Let present age of son as x then present age of father is 4x .

$\green{ \large \underline{ \mathbb{\underline{AGES \: AFTER \: 5 \: YEARS: }}}}$

• After 5 years age of father = 4x + 5

• After 5 years age of son = x + 5

$\green{ \sf \underline{ \mathbb{\underline{ACCORDING \: TO \: QUESTION: }}}}$

$\\ \displaystyle \bf \longrightarrow 4x + 5 = 3(x + 5) \\ \\ \displaystyle \bf \longrightarrow4x + 5 = 3x + 15 \\ \\ \displaystyle \bf \longrightarrow4x - 3x = 15 - 5 \\ \\ \displaystyle \bf \longrightarrow x = 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\purple{ \boxed{ \begin{array}{l} \textsf{Present age of son = x = 10 years} \\ \\\textsf{Present age of father = 4x = 40 years} \end{array}}}$