Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 2

If $\frac{\mathrm{x}}{2}=\frac{\mathrm{y}}{3}=\frac{\mathrm{z}}{7}$ then what is the value of $\frac{\left(2 \mathrm{x}-3 \mathrm{y}+4 \mathrm{z}\right)}{2\mathrm{y}}$?

If $\mathrm{p} : \mathrm{q} : \mathrm{r} = 2 : 3 : 5$ then what is the value of $\frac{\mathrm{p}+\mathrm{q}+\mathrm{r}}{\mathrm{r}}$?

If $\mathrm{x}:\mathrm{y}=4:5$ and $\mathrm{y}:\mathrm{z}=4:3$ then what is the value of $\mathrm{x}:\mathrm{y}:\mathrm{z}$?

If $\mathrm{x}:\mathrm{y}=3:2$ and $\mathrm{y}:\mathrm{z}=4:3$ then what is the value of $\mathrm{x}:2\mathrm{z}$?

If $\mathrm{a}:\mathrm{b}=\mathrm{b}:\mathrm{c}$ then show that, $\mathrm{a}:\mathrm{c}={\mathrm{a}}^2:{\mathrm{b}}^2$

If $4{\mathrm{x}}^2+9{\mathrm{y}}^2=12\mathrm{xy}$ then $\mathrm{x}:\mathrm{y}$ is

If the four numbers $\mathrm{x}, 2\mathrm{x}, 3 \& \mathrm{y}$ are in proportion the value of $\mathrm{y}$ will be

What numbers must be subtracted from the numbers $5, 9$ and $21$ so that the resulting numbers are in continued proportion?