Question

Mark the correct alternative in the following question:

$$\begin{gathered} \mathrm{If}x:y=1:1,\mathrm{then}\frac{3x+4y}{5x+6y}= \\ \left(\mathrm{a}\right)\frac{7}{11}\left(\mathrm{b}\right)\frac{17}{11}\left(\mathrm{c}\right)\frac{17}{23}\left(\mathrm{d}\right)\frac{4}{5} \end{gathered}$$

Answer 1

$$\begin{gathered} \mathrm{As},x:y=1:1 \\ \Rightarrow \frac{x}{y}=\frac{1}{1} \\ \Rightarrow x=y \\ \mathrm{Now}, \\ \frac{3x+4y}{5x+6y} \\ =\frac{3x+4x}{5x+6x}\left(\mathrm{As},x=y\right) \\ =\frac{7x}{11x} \\ =\frac{7}{11} \end{gathered}$$

Hence, the correct alternative is option (a).