Question

The present age of Tamanna's mother is four times that of Tamanna's age. Tamanna's age ten years from now will be half of her mother's present age. What are their present ages?

Answer 1

Let their ages be m and t, respectively. Currently, m = 4t.

In ten years: t+10 = (1/2)(m+10).

Multiplying both sides by 2, we get 2t + 20 = m + 10. Substituting 4t for m produces

2t + 20 = 4t + 10. Then 10 = 2t, and t=5. Tamanna is currently 5 years old, and her mother is 20.

Answer 2

$m = 4t$
$\frac{1}{2} m = t + 10$
If we put the first equation into the second one

$\frac{1}{2} (4t) =t + 10$
Which means

$t = 10$
Tamanna is 10 years old, her mother is 40