Question

The value of $x:y$ is _____, if $(4x+7y):(5x-y)$ is the duplicate ratio of $5:1$

• A. $32:121$
• B. $25:1$
• C. $1:5$
• D. $1:25$

Answer 1

The correct option is A $32:121$

$(4x+7y):(5x-y)$ is the duplicate ratio of $5:1$.
Also, the duplicate ratio of $5:1$ is $25:1$.
$\therefore \frac{4x+7y}{5x-y}=\frac{25}{1}\Rightarrow 4x+7y=125x-25y$
$\therefore 125x-4x=7y+25y$
$\therefore 121x=32y$
$\therefore \frac{x}{y}=\frac{32}{121}$
$\therefore x:y=32:121$