The ratio between the ages of a father and a son at present is 5 : 2, respectively. Four years, hence the ratio between the ages of the son and his mother will be 1 : 2 respectively. What is the ratio between the present ages of the father and the mother respectively?

A box contains one rupee, fifty paisa and twenty five paisa coins. The total number of coins are $378$. The ratio of values of the above coins is $13:11:7$. The number of twenty five paise coins was:

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

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

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:

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

Using properties of proportion solve for $x$, given

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

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