Question

Sushma is 15 years older than Vijay, but in 3 more years she will be 8 times as old as Vijay was 3 years ago. How old are they now?​

Answer 1

Answer:

Given :-

• Sushma is 15 years older than Vijay, but in 3 more years she will be 8 times as old as Vijay was 3 years ago.

To Find :-

• How old are they now.

Solution :-

Let,

$\mapsto \bf Present\: Age\: Of\: Vijay =\: x\: years$

$\mapsto \bf Present\: Age\: Of\: Sushma =\: (x + 15)\: years$

According to the question,

$\implies \sf (x + 15) + 3 =\: 8(x - 3)$

$\implies \sf x + 15 + 3 =\: 8x - 24$

$\implies \sf x + 18 =\: 8x - 24$

$\implies \sf x - 8x =\: - 24 - 18$

$\implies \sf {\cancel{-}} 7x =\: {\cancel{-}} 42$

$\implies \sf 7x =\: 42$

$\implies \sf x =\: \dfrac{42}{7}$

$\implies \sf\bold{\purple{x =\: 6}}$

Hence, the present age of Vijay and Sushma are :

❒ Present Age Of Vijay :

$\longrightarrow \sf Present\: Age_{(Vijay)} =\: x\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Vijay)} =\: 6\: years}}$

❒ Present Age Of Sushma :

$\longrightarrow \sf Present\: Age_{(Sushma)} =\: (x + 15)\: years$

$\longrightarrow \sf Present\: Age_{(Sushma)} =\: (6 + 15)\: years$

$\longrightarrow \sf\bold{\red{Present\: Age_{(Sushma)} =\: 21\: years}}$

${\small{\bold{\underline{\therefore\: The\: present\: age\: of\: Vijay\: and\: Sushma\: are\: 6\: years\: and\: 21\: years\: respectively\: .}}}}$

Answer 2

Given : Sushma is 15 years older than Vijay, but in 3 more years will be 8 times as old as Vijay was 3 years ago.

To Find : Find the old are they now ?

_________________________

Solution : Let the age of Vijay be x years.

$~$

• Then the age of Sushma is 15 years older than Vijay = (x + 15) years.
• 3 years she will be 8 times as old as Vijay was 3 years ago.

$~$

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

$~$

$\qquad{\sf:\implies{(x~+~15)~+~3~=~8(x~-~3)}}$

$\qquad{\sf:\implies{x~+~15~+~3~=~8x~-~24}}$

$\qquad{\sf:\implies{x~+~18~=~8x~-~24}}$

$\qquad{\sf:\implies{7x~=~42}}$

$\qquad{\sf:\implies{x~=~\cancel\dfrac{42}{7}}}$

$\qquad:\implies{\underline{\boxed{\frak{\pink{\pmb{x~=~6}}}}}}$★

$~$

Therefore,

• If Vijay's present age is 6 years, Then the age of Sushma = (x + 15) => 21 years.

$~$

Hence,

$\therefore\underline{\sf{The~age~of~Vijay~is~\bf{\underline{\pmb{6~years}}}~\sf{\&}~\sf{The ~age~ of ~Sushma ~is~\bf{\underline{\pmb{21~years}}}}}}$