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The ratio of two positive numbers is $2:3.$ If $10$ and the sum of the numbers are added to their product, square of $16$ is obtained. The greater number is :

1. $6$
2. $9$
3. $12$
4. $18$

Assume that numbers are $2x,3x$. Now according to the question:

$(2x \times 3x) + 3x+2x+10=256$

$\implies6x^2+5x-246=0\implies x=6$

So the number are: $6\times 2=12,6\times 3=18$

Option (D) is correct.
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