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Let the Sumit's and Prakash's age at present is $2x$ years and $3x$ years respectively.

Sumit is $6$ years younger than Prakash, so $2x = 3x-6$

$\implies x = 6$

$\therefore$ The present age of Sumit $ = 2x = 12$ years and the present age of Prakash $ = 3x = 18$ years.

Now, the ratio of Sumit's age to Prakash's age after six years will be $ = \dfrac{12+6}{18+6} = \dfrac{18}{24}  = \dfrac{3}{4}$

Hence, The ratio of Sumit's age to Prakash's age after six years will be $3:4.$

So, the correct answer is $(C).$
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