Question

What quantity must be added to each term of the ratio $x:y$ so that it may become equal to $c:d$ ?

Answer 1

Step: Find the term

Let $z$ to be added to each term of $x:y$

$\therefore \frac{x+z}{y+z}=\frac{c}{d}$

$\Rightarrow d(x+z)=c(y+z)$

$\Rightarrow dx+dz=cy+cz$

$\Rightarrow dz-cz=cy-dx$

$\Rightarrow z(d-c)=cy-dx$

$\therefore z=\frac{cy-dx}{d-c}$

Hence, the term $\frac{cy-dx}{d-c}$ is added.