Question

The present age of Jayesh is one-third the age of his father. Eight years ago , Jayesh’s father was five times as old as Jayesh. Find their present ages.

Answer 1

❍ Let's Consider the Present age of Jayesh father's be x yrs .

⠀⠀⠀⠀⠀Given that For Present age of Jayesh ,

⠀⠀》The present age of Jayesh is one-third the age of his father .

$\qquad:\implies \sf Jayesh _{(Present \:age\:)} \:=\: \dfrac{1}{3} \: \:of \:\:Father's \:age \:$

$\qquad:\implies \sf Jayesh _{(Present \:age\:)} \:=\: \dfrac{1}{3} \: \times \:\: x \:$

$\qquad:\implies \sf Jayesh _{(Present \:age\:)} \:=\: \dfrac{1(x)}{3} \: \:$

$\qquad:\implies \sf Jayesh _{(Present \:age\:)} \:=\: \dfrac{x}{3} \: \:$

$\qquad :\implies \pmb{\underline{\purple{\: Jayesh _{(Present \:age\:)} \:=\: \dfrac{x}{3} \:yrs}} }\:\: \bigstar$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀☆ BEFORE 8 YEARS their ages :

• Jayesh age will be ( x/3 - 8 ) yrs
• Jayesh father's age will be ( x - 8 ) yrs

⠀⠀⠀⠀⠀⠀$\underline {\boldsymbol{\star\:According \:to \: the \: Question \::}}$

⠀⠀⠀⠀⠀━━━ Eight years ago , Jayesh’s father was five times as old as Jayesh.

$\qquad \dashrightarrow \sf 5 \times \:Jayesh \: \:age _{(Eight \:Year\:ago\:)} \: =\:\:Jayesh\:\:father's \:age\:_{(Eight \:Years \:ago\:)} \:$

$\qquad \dashrightarrow \sf 5 \times \: \bigg( \:\:\dfrac{x}{3} - 8 \bigg) \: = \:x - 8 \:$

$\qquad \dashrightarrow \sf \:\:\dfrac{5x}{3} - 40 \: = \:x - 8 \:$

$\qquad \dashrightarrow \sf \:\:\dfrac{5x}{3} - 40 + 8 \: = \:x \:$

$\qquad \dashrightarrow \sf \:\:\dfrac{5x}{3} - 32 \: = \:x \:$

$\qquad \dashrightarrow \sf \:\:\dfrac{5x - 32 \times 3 }{3} \: = \:x \:$

$\qquad \dashrightarrow \sf \:\:\dfrac{5x - 96 }{3} \: = \:x \:$

$\qquad \dashrightarrow \sf \:\:5x - 96 \: = \:x \times 3 \:$

$\qquad \dashrightarrow \sf \:\:5x - 96 \: = \:3x \:$

$\qquad \dashrightarrow \sf \:\: - 96 \: = \:3x - 5x \:$

$\qquad \dashrightarrow \sf \:\: - 96 \: = \:-2x \:$

$\qquad \dashrightarrow \sf \:\: 96 \: = \:2x \:$

$\qquad \dashrightarrow \sf \:\: 2x \: = \:96 \:$

$\qquad \dashrightarrow \sf \:\: x \: = \:\dfrac{96}{2} \:$

$\qquad \dashrightarrow \sf \:\: x \: = \:48 \:$

$\qquad \dashrightarrow \pmb{\underline{\purple{\:x = 48 \:yrs }} }\:\:\bigstar$

• Here , x denotes Present age of Jayesh father which is 48 yrs

⠀⠀⠀⠀⠀⠀AND ,

• Present age of Jayesh is x/3 = 48 / 3 = 16 yrs .

⠀⠀⠀⠀⠀$\therefore {\underline{ \sf \:Hence, \:Present \:ages \:of\:Jayesh \:and\:Jayesh \:Father\:is\:\bf 48 \:\:yrs \:\:\&\:\:16\:yrs\:\sf\:, respectively. \:}}$