Question

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

Answer 1

Corrected Question :

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

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Given : Present age of Jayesh.

To Find : Present ages ?

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❍ Let's consider the Present age of Jayesh father's be x years.

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

$~~~~~~~~~~{\sf:\implies{Jayesh_{(Present ~age)}~=~\dfrac{1}{3}~of~Father's~age}}$

$~~~~~~~~~~{\sf:\implies{Jayesh_{(Present~age)}~=~\dfrac{1}{3}~×~x}}$

$~~~~~~~~~~{\sf:\implies{Jayesh_{(Present~age)}~=~\dfrac{1(x)}{3}}}$

$~~~~~~~~~~{\sf:\implies{Jayesh_{(Present~age)}~=~\dfrac{x}{3}}}$

$~~~~~~~~~~:\implies{\underline{\boxed{\frak{\pink{Jayesh_{(Present~age)}~=~\dfrac{x}{3} years}}}}}$

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Therefore,

• BEFORE 8 YEARS their ages :

• Jayesh age will be (x/3 - 8) years

• Jayesh age will be (x - 8) years

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$\underline{\frak{According ~to ~the ~Given~Question~:}}$

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• $\leadsto$ Eight years ago, Jayesh's father was five times as old as Jayesh.

$~~~~~~~~~~{\sf:\implies{5~×~Jayesh~age_{(Eight~Years~ago)}~=~Jayesh~father's~age_{(Eight~Years~ago)}}}$

$~~~~~~~~~~{\sf:\implies{5~×~\bigg(\dfrac{x}{3} - 8\bigg)~=~x~-~8}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{5x}{3} - 40~=~x~-~8}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{5x}{3} - 40~+~8~=~x}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{5x}{3} - 32~=~x}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{5x~-~32×~3}{3}~=~x}}$

$~~~~~~~~~~{\sf:\implies{\dfrac{5x~-~96}{3}~=~x}}$

$~~~~~~~~~~{\sf:\implies{5x~-~96~=~x~×~3}}$

$~~~~~~~~~~{\sf:\implies{5x~-~96~=~3x}}$

$~~~~~~~~~~{\sf:\implies{-96~=~3x~-~5x}}$

$~~~~~~~~~~{\sf:\implies{-96~=~-2x}}$

$~~~~~~~~~~{\sf:\implies{96~=~2x}}$

$~~~~~~~~~~{\sf:\implies{2x~=~9x}}$

$~~~~~~~~~~{\sf:\implies{x~=~\dfrac{96}{2}}}$

$~~~~~~~~~~{\sf:\implies{x~=~\cancel\dfrac{96}{2}}}$

$~~~~~~~~~~{\sf:\implies{x~=~48}}$

$~~~~~~~~~~:\implies\underset{\blue{\rm Required\ Answer}}{\underbrace{\boxed{\pink{\frak{x~=~48~years}}}}}$

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• Here, x denotes Present age of Jayesh father which is 48 years & Present age of Jayesh is x/3 = 48/3 = 16 years.

Hence,

$\therefore\underline{\sf{The~present~ages~of~Jayesh~and~Jayesh~Father~\sf{is}~\bf{48~years~\&~16~years}}}$

$~~~~$$\qquad\quad\therefore\underline{\textsf{\textbf{Hence Verified!}}}$