Question

If $\frac{3x-4y}{2x-3y}=\frac{5x-6y}{4x-5y}$, find x : y.

• A. 1:1
• B. 2:2
• C. 3:3
• D. 4:4

Answer 1

The correct option is A

1:1

$\frac{3x-4y}{2x-3y}=\frac{5x-6y}{4x-5y}$
By cross multiplication, we get
$12x^2-15xy-16xy+20y^2=10x^2-15xy-12xy+18y^2\Rightarrow 12x^2-31xy+20y^2=10x^2-27xy+18y^2\Rightarrow 10x^2-27xy+18y^2-12x^2+31xy-20y^2=0\Rightarrow -2x^2+4xy-2y^2=0\Rightarrow x^2-2xy+y^2=0\Rightarrow (x-y{)}^2=0\Rightarrow x-y=0\Rightarrow x=y$
Hence, $x:y=1:1$