Question

If $12x+15y=249$ and $5x+13y=124$, then the value of $\frac{y}{x}$ is.

• A. $\frac{17}{3}$
• B. $\frac{3}{17}$
• C. $\frac{13}{7}$
• D. $\frac{7}{13}$

Answer 1

Answer: (B)

$\frac{3}{17}$

Given equations are $12x+15y=249$ and $5x+13y=124$

$\therefore$ equation can be written as $4x+5y=83$.

Hence, consider the equations $4x+5y=83$ .... (i)

and $5x+13y=124$ .... (ii)

Multiplying eqn (i) by $5$ and eqn (ii) by $4$, we get

$20x+25y=415$ and $20x+52y=496$

Subtracting the two equations gives us $y=3$

Substituting this value of $y$ in eqn (i), we get $x=17$

Hence, $\frac{y}{x}=\frac{3}{17}$