Answer :
Consider that 'n' is the numerator, and 'd' is the denominator of the fraction.
Given that the ratio of numerator to denominator is 1 to 3,
[tex]\begin{gathered} \frac{n}{d}=\frac{1}{3} \\ \Rightarrow d=3n \end{gathered}[/tex]Given that if the numerator and denominator are both increased by 2, the fraction is now equal to 3/4,
[tex]\begin{gathered} \frac{n+2}{d+2}=\frac{3}{4} \\ 4(n+2)=3(d+2) \\ 4n+8=3d+6 \end{gathered}[/tex]Thus, the required system of equations is,
[tex]\begin{gathered} d=3n \\ 4n+8=3d+6 \end{gathered}[/tex]Therefore, first option is the correct choice.