Question : If x : y = 3 : 4, then the value of $\frac{5x-2y}{7x+2y}$ is:
Option 1: $\frac{7}{25}$
Option 2: $\frac{7}{23}$
Option 3: $\frac{7}{29}$
Option 4: $\frac{7}{17}$
Correct Answer: $\frac{7}{29}$
Solution :
$x : y=3:4$
$⇒\frac{x}{y}=\frac{3}{4}$
Now, $\frac{5x-2y}{7x+2y}=\frac{5\frac{x}{y}-2}{7\frac{x}{y}+2}$
Putting $\frac{x}{y} = \frac{3}{4}$ in above equation, we get,
$=\frac{5\times \frac{3}{4}-2}{7\times \frac{3}{4}+2}$
$=\frac{15-8}{21+8}$
$=\frac{7}{29}$
Hence, the correct answer is $\frac{7}{29}$.
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