Ratio and Proportion

If $\frac{a_1^2+a_2^2}{a_1^2-a_2^2}=\frac{5}{3}$, then find $\frac{a_2}{a_1}$

If $p, q$ and $r$ are positive real numbers, then the quantity $\frac{(p+r)}{(q+r)}$ is:

Let $Q=\left(\frac{x}{y}\right)$ where $x$ and $y$ are positive real numbers. If both $x$ and $y$ are increased equally, then

If $x+7:2\left(x+14\right)$ is the duplicate ratio of $5:8,$ then $x$ is

Find the compounded ratio of the ratio $2a:3b$ and the duplicate ratio of $9b^2:ab$.

If $a, b, c, d$ are in proportion, then

$\frac{1}{7}$ is the incommensurable quantity.

Identify the incommensurable quantity from the below options.

$\frac{\sqrt{3}}{2}$ is the incommensurable quantity.

Identify the incommensurable quantity from the below options.

Describe the concept of incommensurable quantities.

If$₹800$ when divided in the ratio of $3:5$ is $₹ k \text{and} ₹ m$, then the value of $k+m$ is

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

$81 \mathrm{kg}:45 \mathrm{kg}::18$ men : $10$ men

$60 \mathrm{p}:₹3=1:5$

The numbers $6, 10, 14$ and $22$ are in proportion.

Find the value of $\mathrm{n}$, if $\mathrm{n}:15::4:30$.

If$(x+3):(4x+1)$ is the duplicate ratio of $3 : 5,$ then find the value of $x$.