Question

Present age of Raj is twice that of Rashmi 10 years ago, his age was three times the age
of Rashmi. Find their present ages.​

Answer 1

$\huge\underline\mathrm{Question-}$

Present age of Raj is twice that of Rashmi 10 years ago, his age was three times the age of Rashmi. Find their present ages.

$\huge\underline\mathrm{Answer-}$

Present Age of rashmi = 20 years

Present Age of raj =

$\huge\underline\mathrm{Explanation-}$

Let age of raj be x

age if rashmi be y

According to the question,

• x = 2y

10 yrs ago,

age of raj = x - 10

age of rashmi = y - 10

• (x-10) = 3(y-10)

$\mapsto$ x - 10 = 3y - 30

$\mapsto$ x - 10 - 3y + 30 = 0

$\mapsto$ x - 3y = -20

put x = 2y

$\mapsto$ 2y - 3y = -20

$\mapsto$ $\cancel{-}$ y = $\cancel{-}$ 20

$\mapsto$ y = 20

$\therefore$ Present Age of rashmi is 20 years.

Now put y = 20 in ( x = 2y )

$\mapsto$ x = 2 × 20

$\mapsto$ x = 40

$\therefore$ Present age of raj is 40 years.

Answer 2

Answer:

${\boxed{\bold{Present\:age\:of\:Raj=40\:years}}}$

${\boxed{\bold{Present\:age\:of\:Rashmi=20\:years}}}$

Step-by-step explanation:

Let the present age of Raj = X years.

And the present age of Rashmi = Y years.

${\underline{\underline{\bold{According\:to\:question:-}}}}$

$\rightarrow\sf X = 2Y .............(eq.1)$

$\rightarrow\sf (X-10)= 3(Y-10) \\\\\rightarrow\sf X - 10 = 3Y - 30 \\\\\rightarrow\sf X = 3Y - 30 + 10 \\\\\rightarrow\sf X = 3Y - 20 \\\\\tt *Putting\:values\:from\:(eq.1) \\\\\rightarrow\sf 2Y = 3Y - 20 \\\\\rightarrow\sf 3Y - 2Y = 20 \\\\\rightarrow{\boxed{\sf{Y = 20\:years}}}$

$\therefore\bold{\underline{Present\:age\:of\:Rashmi=20\:years}}$

$\sf *Putting\:value\:of\:Y\:in\:(eq.1)\:we\:get:-\\\\\rightarrow\sf X = (2 \times 20)\:years \\\\\rightarrow{\boxed{\sf{X = 40\:year}}}$

$\therefore\bold{\underline{Present\:age\:of\:Raj = 40\:years}}$