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Solution

Let Karan’s present age = $K$ years
Let Deepak’s present age = $D$ years

Given:
$K \times D = 240$
and $2D = K + 4 \Rightarrow K = 2D - 4$

Substitute in the first equation:
$(2D - 4)D = 240$
$\Rightarrow 2D^2 - 4D - 240 = 0$
$\Rightarrow D^2 - 2D - 120 = 0$

Solving: $D = \dfrac{2 + \sqrt{484}}{2} = \dfrac{2 + 22}{2} = 12$

Deepak’s present age = $12$ years
Two years ago = $12 - 2 = \mathbf{10}$ years

✅ Final Answer: $10$ years