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. shikha $50$, rani $20$
• B. rani $20$, shikha $50$
• C. rani $30$, shikha $80$
• D. none

Answer 1

Answer: (A)

shikha $50$, rani $20$

Let the present age of Shikha $=x$ years

Let the present age of Rani $=y$ years

Five years ago, Shikha was thrice as old as Rani.

Five years ago, Shikha's age $=x-5$ years

Five years ago, Rani's age $=y-5$ years

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

$x-5=3y-15$

$x-3y-5+15=0$

$x-3y+10=0$ ............ (1)

$10$ years later, Shikha will be twice as old as Rani.

$10$ years later, Shikha's age $=x+10$ years

$10$ years later, Rani's age $=y+10$ years

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

$x+10=2y+20$

$x-2y+10-20=0$

$x-2y-10=0$ ............ (2)

Subtracting equation (2) from (1), we get,

$x-3y+10-(x-2y-10)=0$

$x-3y+10-x+2y+10=0$

$-y+20=0$

$y=20$

From equation (1),

$x-3y+10=0$

$x-3\left(20\right)+10=0$

$x-50=0$

$x=50$

present age of Shikha $=x=50$ years

present age of Rani $=y=20$ years