correct answer is: b) 25 : 39

Explanation

Here,
x\ :\ y=3\ ∶\ 4
\rightarrow\frac{x}{y}=\frac{3}{4}
\rightarrow4x=3y _{[cross multiply]}
\rightarrow x=\frac{3y}{4}
Now,
\left(3x+4y\right):\left(5x+6y\right)
\rightarrow\left(3\times\frac{3y}{4}+4y\right)\ ∶\ \left(5\times\frac{3y}{4}+6y\right) _{[put the value ‘x’]}
\rightarrow\left(\frac{9y}{4}+4y\right)\ ∶\ \left(\frac{15y}{4}+6y\right)
\rightarrow\left(\frac{9y+16y}{4}\right)\ ∶\ \left(\frac{15y+24y}{4}\right) _[L.C.M=4]
\rightarrow\ \frac{25y}{4}\ ∶\ \frac{39y}{4}
\rightarrow\frac{25y}{4}\div\ \frac{39y}{4}
\rightarrow\ \frac{25y}{4}\times\frac{4}{39y}
\rightarrow\frac{25}{39}
\rightarrow\ 25\ ∶\ 39
Ans: 25 : 39