Question

The value of $x$ is ____ if $(3x+1):(5x-4)$ is the duplicate ratio of $5:6$

• A. $2$
• B. $4$
• C. $8$
• D. $6$

Answer 1

The correct option is C $8$

$(3x+1):(5x-4)$ is the duplicate ratio of $5:6$.
Also, the duplicate ratio of $5:6$ is $5^2:6^2=25:36$
$\therefore \frac{3x+1}{5x-4}=\frac{25}{36}$
$\therefore 108x+36=125x-100$
$\therefore 125x-108x=36+100$
$\therefore 17x=136$
$\therefore x=\frac{136}{17}=8$