Question

Five years ago, Shikha was thrice as old as Rani. $10$ years later, Shikha will be twice as old as Rani. How old are they now?

• A. Rani $20$ yrs, Shikha $50$ yrs
• B. Shikha $20$ yrs, Rani $50$ yrs
• C. Shikha $80$ yrs, Rani $30$ yrs
• D. Shikha $30$ yrs, Rani $80$ yrs

Answer 1

The correct option is A Rani $20$ yrs, Shikha $50$ yrs

Let the present age of Shikha and Rani be x and y respectively.

$\therefore$ Given that five years ago, Shikha was thrice as old as Rani.

$\Rightarrow (x-5)=3(y-5)$

$\Rightarrow x-5=3y-15$

$\Rightarrow 3y-x=10⟶\left(i\right)$

Also given that 10 years later, Shikha will be twice as old as Rani.

$\therefore (x+10)=2(y+10)$

$\Rightarrow x+10=2y+20$

$\Rightarrow x=2y+10$

Substituting the value of x in ${eq}^n\left(i\right)$, we have

$3y-(2y+10)=10$

$\Rightarrow 3y-2y-10=10$

$\Rightarrow y=20$

$\because x=2y+10$

$\Rightarrow x=2\times 20+10$

$\Rightarrow x=50$

Hence, present age of Shikha and Rani are 50 and 20 respectively.