Question

If x : y = 1 : 1, then $\frac{3x+4y}{5x+6y}=$

(a) $\frac{7}{11}$
(b) $\frac{17}{11}$
(c) $\frac{17}{23}$
(d) $\frac{4}{5}$

Answer 1

It is given that,
$\frac{x}{y}=\frac{1}{1}=1$ ...(1)

Now,
$$\begin{gathered} \frac{3x+4y}{5x+6y}=\frac{\left(3x+4y\right)÷y}{\left(5x+6y\right)÷y} \\ =\frac{3\left({\displaystyle \frac{x}{y}}\right)+4}{5\left({\displaystyle \frac{x}{y}}\right)+6} \\ =\frac{3\left(1\right)+4}{5\left(1\right)+6}\left[\mathrm{From}\left(1\right)\right] \\ =\frac{3+4}{5+6} \\ =\frac{7}{11} \end{gathered}$$

Hence, the correct option is (a).