Question

Arna is twice as old as Mae. In 4 years time, she will be five-thirds as old as Mae. How old is each now

with explanation pls

Answer 1

Let Mae's current age be x years.

Since Arna is twice as old as Mae, Arna's present age is 2x years.

After 4 years, Mae's age will be x+4 years and Arna's age will be 2x+4 years.

As per given information, after 4 years, Arna will be five-thirds as old as Mae.

Thus, the equation is:

$2x + 4 = \frac{5}{3}*(x+4)$

$\therefore 3 * (2x+4) = 5*(x+4)$

$\therefore 6x + 12 = 5x + 20$

$\therefore 6x - 5x = 20 - 12$

$\therefore x = 8$

Hence 2x = 2 * 8 = 16 years

Thus, Mae's current age is 8 years and Arna's current age is 16 years.