The cost and revenue functions of a product are given by $C(x) = 20x + 4000$ and $R(x) = 60x + 2000$ respectively,where $x$ is the number of items produced and sold. The value of $x$ to earn profit is

The set of all real numbers $x$ for which ${x^2} - |x + 2| + x > 0$ is

Find the sum of all integral values of $a$ such that the equation $||x - 2| - |3 - x|| = 2 - a$ has a solution.

The longest side of a triangle is twice the shortest side and the third side is $2 \text{ cm}$ longer than the shortest side. If the perimeter of the triangle is more than $166 \text{ cm}$, then find the minimum length of the shortest side. (in $\text{ cm}$)

In drilling the world's deepest hole,it was found that the temperature $T$ in degrees Celsius,$x \text{ km}$ below the earth's surface,is given by $T = 30 + 25(x - 3)$,where $3 \leq x \leq 15$. At what depth will the temperature be between $155^{\circ}C$ and $205^{\circ}C$?

$A$ manufacturer has $600 \text{ litres}$ of a $12 \%$ solution of acid. How many litres of a $30 \%$ acid solution must be added to it so that the acid content in the resulting mixture will be more than $15 \%$ but less than $18 \%$?