Average weight of 10 boys is more than the average weight of 15 girls by 5 kg. If the total weight of the 10 boys is 550 kg, what is the average weight of the 10 boys and 15 girls together?

Using properties of proportion, solve for $x$, where $x$ is a positive number:

$\frac{2x+\sqrt{4x^2-1}}{2x-\sqrt{4x^2-1}}=4$

In water, The ratio of the mass of hydrogen to the mass of oxygen is always _____.

Using properties of proportion solve for $x$, given

$\frac{\sqrt{5x}+\sqrt{2x-6}}{\sqrt{5x}-\sqrt{2x-6}}=4$

If $\frac{\left[a+b-c\right]}{\left[a+b\right]}=\frac{\left[b+c-a\right]}{\left[b+c\right]}=\frac{\left[c+a-b\right]}{\left[c+a\right]}$ and $a+b+c\ne 0$ then prove that $a=b=c$.

Using properties of proportion find $x:y$, given:

$\frac{x^2+2x}{2x+4}=\frac{y^2+3y}{3y+9}$

Average of three numbers $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ is $1$ more than the average of $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. Average of $\mathrm{A}$ and $\mathrm{D}$ is $19.5$.

Quantity $1$: Find $\mathrm{A}$.

Quantity $2$: $21$.