Question

If $x:y=4:5$, then $(4x+5y):(5x-2y)$ is equal to:

• A. $41:10$
• B. $4:5$
• C. $16:25$
• D. $3:10$

Answer 1

The correct option is A $41:10$

We have, $x:y=4:5$
$\Rightarrow 5x=4y\Rightarrow x=\frac{4y}{5}$ .......... $\left(i\right)$
Now, $(4x+5y):(5x-2y)$
$=\left[4\left(\frac{4}{5}\right)y+5y\right]:\left[5\left(\frac{4}{5}y\right)-2y\right]$ ..... (using $\left(i\right)$)
$=\left(\frac{16}{5}y+5y\right):(4y-2y)$
$=\frac{41}{5}y:2y=41:10$.