Question

If $4x+5y=83$ and $3x:2y=21:22$, then \(y - x)\ equals:

• A. 3
• B. 4
• C. 7
• D. 11
• E. None of the above

Answer 1

The correct option is B 4

$\frac{3x}{2y}=\frac{21}{22}$
$\Rightarrow \frac{x}{y}=\frac{21}{22}\times \frac{2}{3}=\frac{7}{11}$ $\Rightarrow \frac{x}{7}=\frac{y}{11}=k$
Now, according to the question
$4x+5y=83$
$\Rightarrow 4\times 7k+5\times 11k=83$
$\Rightarrow 28k+55k=83$
$\Rightarrow 83k=83\Rightarrow k=1$
$\Rightarrow x=7$ and $y=11$
$\therefore y-x=11-7=4$