$A$ person's present age is two-fifth of the age of his mother. After $8$ years,he will be one-half of the age of his mother. How old is the mother at present (in $years$)?

In two alloys,gold and silver are in the ratios of $4:1$ and $1:3$. After alloying together $10 \text{ kg}$ of the first alloy,$16 \text{ kg}$ of the second,and several kilograms of pure gold,an alloy was obtained in which the ratio of gold to silver was $3:2$. Find the weight of the new alloy (in $\text{kg}$).

The third proportional to $0.8$ and $0.2$ is

The reciprocals of the square of the numbers $1 \frac{1}{2}$ and $1 \frac{1}{3}$ are in the ratio:

There is a ratio of $5:4$ between two numbers. If $40\%$ of the first number is $12$,then $50\%$ of the second number is:

Three numbers are in the ratio of $3:2:5$ and the sum of their squares is $1862$. The smallest of these numbers is: