Rohan's grandmother is five times his age. After 10 years from now, his grandmother will be three times his age. How old are they at present?

Question

Rohan's grandmother is five times his age. After 10 years from now, his grandmother will be three times his age. How old are they at present?

Answer 1

suppose Rohan's grandmother's age is $y$ and Rohan's age is $x$. Then you get:

$y= 5x$

$y+10 = 3(x+10)$

Substitute the first into the second,

$5x+10 = 3x + 30$

which gives $2x = 20$ or $x = 10$

Thus, Rohan's current age is $10$ and his grandmother's current age is $50$.

$10$ years from now, they will be $20$ and $60$ respectively.

Answer 2

Currently, G = 5R ---- (1)

(Where G = Grandmom's age, and R = Rohan's age)

After 10 years, G + 10 = 3 (R + 10) ==> G + 10 = 3R + 30 ==> G = 3R + 20 ---- (2)

Solving equations (1), and (2)... 5R = 3R +20 ==> R = 10 ----(3)

Substituting (3) in (1), will give G as 50.

Therefore, Rohan is 10 years old, and Grandmother is 50 years old (Current ages)

Answer 3

Assume the ages are integers, let $y$ be the current age of the grandma, and $y+10$ be her age in $10$ years time. Then $5|y$ and $3|(y+10)$. For this to happen $y=5(3k+1)$, with $y+10=5(3k+1)+10=5(3k+3)=3(5k+5)$. So we want $5k+5-(3k+1)=10$, so $2k=6$ so $k=3$. So Rohan's age is $3\cdot3+1=10$ and grandma's age is $5(3\cdot3+1)=50$.