Ratio and Proportion

The central angles $p, q, r$ and $s$ (in degrees) of four sectors in a Pie Chart satisfy the relation $9p=3q=2r=6s$. What is the value of $4p-q$?

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

If $\frac{1}{2}=\frac{4}{8}$, what type of proportion it depicts?

A can contains a mixture of two liquids $A$ and $B$ in the ratio $7:5.$ When $9$ litres of mixture are drawn off and the can is filled with $B\mathit{,}$ the ratio $A$ and $B$ becomes $7:9.$ How many litres of liquid $A$ was contained by the can initially?

Identify the incommensurable quantity from the below options.

Identify the incommensurable quantity from the below options.

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.

Consider the following statements
I. $\underset{n\to \infty }{\lim }\frac{2^n+(-2{)}^n}{2^n}$ does not exist
II. $\underset{n\to \infty }{\lim }\frac{3^n+(-3{)}^n}{4^n}$ does not exist
Then

The number of ordered pairs $\left(x,y\right)$ of positive integers satisfying $2^x+3^y=5^{xy}$ is

If $a, b, c, d$ are in continued proportion and $\left(a^2+b^2+c^2\right)\left(b^2+c^2+d^2\right)={\lambda }^2$, then $\lambda$ is equal to

The third proportional to $\frac{x}{y}+\frac{y}{x}$ and $\frac{x}{y}$ is

The fourth proportional to $3, 5, 27$ is

If $ax+by+cz=a^{2}x+b^{2}y+c^{2}z=0$ and $x+y+z+\left(b-c\right)\left(c-a\right)\left(a-b\right)=0$, then the value of $\frac{x}{bc}+\frac{y}{ac}+\frac{z}{ab}$ is equal to

If $7yz+3zx=4xy, 21yz-3zx=4xy$ and $x+2y+3z=19$, then the ordered triplet $\left(x,y,z\right)$ can be

If $x+y=z, 3x-2y+17z=0$ and $x^3+3y^3+2z^3=167$, then $x+y+z$ is equal to