Question

3.
Ankur is now one-third the age of his father. Twelve years hence he will be half
the age of his father. Determine the present age of Ankur and that of his father.​

Answer 1

Solution :-

Let :-

Present age of father = x

Present age of Ankur = y

12 years hence :-

Age of father = x +  12

Age of Ankur = y + 12

According to the first condition :-

$\longrightarrow \sf y = \dfrac{1}{3} x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(1)$

According to the second condition :-

$\longrightarrow \sf \dfrac{1}{2} \times (x+12) = y+12 \\\\\longrightarrow x+12 = 2(y+12) \\\\\longrightarrow x+12 = 2y+24 \\\\\longrightarrow x-2y = 24-12 \\\\\longrightarrow x-2y = 12 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ......................(2)$

Substitute the value of y in eq (2) :-

$\longrightarrow \sf x- 2 \times \dfrac{1}{3}x = 12 \\\\\longrightarrow x-\dfrac{2x}{3} = 12 \\\\\longrightarrow \dfrac{3x-2x}{3} = 12 \\\\\longrightarrow 3x-2x = 36 \\\\\longrightarrow \bf x = 36$

Substitute x = 36 in eq (1) :-

$\longrightarrow \sf y = \dfrac{1}{3} \times 36 \\\\\longrightarrow \bf y = 12$

Present age of father = 36 years

Present age of Ankur = 12 years