Introduction to Ratio and Proportion

If $a:b=4:5$ find the value of $\left(3a-2b\right):\left(3a+2b\right)$

If $\left(2a+b+4c+2d\right)\left(2a-b-4c+2d\right)=\left(2a-b+4c-2d\right)\left(2a+b-4c-2d\right)$, prove that $\frac{a}{b}=\frac{c}{d}$.

If $\frac{2x+3y}{2y}=\frac{7}{4}$ then by property of  Dividendo, we can write as 

If any four numbers are in proportion and if the second and third term interchange their places, then the four terms are in proportion.

By Alternendo Property, for four numbers $a, b, c, d$ if $a:b=c:d$, then _____ $=b:d$.

By Invertendo property, if two ratios are equal, then their inverse ratios are not equal.

If $\frac{{\mathrm{a}}^2+{\mathrm{b}}^2}{{\mathrm{c}}^2+{\mathrm{d}}^2}=\frac{\mathrm{ab}}{\mathrm{cd}}$, then find the value of $\frac{\mathrm{a}+\mathrm{b}}{\mathrm{a}-\mathrm{b}}$ in terms of $\mathrm{c} \text{and} \mathrm{d}$ only.

If $\frac{x+y}{x-y}=\frac{a}{b}$, then show that $\frac{x^2+xy}{xy-y^2}=\frac{a^2+ab}{ab-b^2}$

If $y$ is the mean proportion of $x$ and $z$ then, proved that $\frac{x^2-y^2+z^2}{x^{-2}-y^{-2}+z^{-2}}=y^4$

If $ab:cd={\left(a+b\right)}^2:{\left(c+d\right)}^2$ then, show that $a:b=c:d$ or, $a:b=d:c$

$a, b, c$ are in continued proportion, prove that, $a:c=\left(a^2+ab+b^2\right):\left(b^2+bc+c^2\right)$

$a, b, c$ are in continued proportion, prove that, $a:c=\left(a^2+b^2\right):\left(b^2+c^2\right)$

If $a,b,c,d$ are in continued proportion, prove that ${\left(a+b+c\right)}^2 : {\left(b+c+d\right)}^2=a^2+b^2+c^2 : b^2+c^2+d^2$.

If $\frac{x^3+3x{y}^2}{3x^{2}y+y^3}=\frac{a^3+3a{b}^2}{3a^{2}b+b^3}$, then $\frac{x}{a}=\frac{y}{b}$.

If $y+x=3\left(y-x\right)$, then $x:y=$_____

What is the third proportional to $4 \& 18$?

Put the number in $\text{'}*\text{'}$ position so that $*, 30, 45$ are in continued proportion.

The numbers $12, 20, 15 \& 25$ are in proportion.

If $x^2+y^2=2xy$, then $x:y=1:2$

If $x=\frac{4ab}{a+b}$ then the value of $\frac{x+2a}{x-2a}+\frac{x+2b}{x-2b}$ is