A product costs $C = \$500$. It is marked up by $40\%$. A $10\%$ discount is then applied to the marked price. Finally, a $15\%$ tax is applied to the discounted price. What is the final selling price?
A pump is used to fill a tank of capacity $1.2$ kL (kilolitres). The flow rate of the pump is $200$ Litres per minute. Calculate the time required to fill the tank, in seconds.
Sarah spent $\frac{1}{3}$ of her initial savings on rent. She then spent $\frac{1}{4}$ of the remaining money on groceries. If she had $\$90$ left after these expenditures, how much money did she start with?
A student scored $85, 92,$ and $78$ on the first three equally weighted tests. To achieve an overall average score of $88$ across five tests, what average score must they achieve on the remaining two tests?
Three friends, X, Y, and Z, share profits in the ratio $3:5:2$. If X gives $20\%$ of his share to Z, what is the new simplified ratio X:Y:Z?
A rectangular prism has a volume of $60 \text{ cm}^3$ and a height of $6 \text{ cm}$. The length of the base is $3 \text{ cm}$ longer than the width ($W$). If the width is $W = x \text{ cm}$, what is the perimeter of the base in cm?
Evaluate the following expression: $\frac{0.75 + 1\frac{1}{2}}{30\% \times 2}$
A hall is open from 9:00 AM to 5:00 PM. A drama group meets every $45$ minutes, starting at $9:15$ AM. A pottery class meets every hour, starting at $9:45$ AM. How many times do both activities start simultaneously between $9:00$ AM and $5:00$ PM?
A baker produces two types of cakes, Deluxe (D) and Standard (S). Deluxe requires $2$ hours of preparation and $1$ hour of decoration. Standard requires $1$ hour of preparation and $3$ hours of decoration. $10$ hours of preparation and $15$ hours of decoration are available. If profit is $\$10$ per Deluxe cake and $\$12$ per Standard cake, what is the maximum possible profit?
Four employees (A, B, C, D) completed a task sequentially on different days: Monday, Tuesday, Wednesday, Thursday. B completed the task immediately before C. D did not complete the task on Monday or Thursday. A completed the task after C. What day did D complete the task?
Simplify the expression: $-1.5 - (-4.2) + 0.3$.
A commodity's price is increased by $25\%$. Subsequently, the new price is subjected to a further reduction of $X\%$. If the net effect of these two successive changes is an overall decrease of $5\%$ from the original price, what is the value of $X$?
The cost prices of Item A and Item B are in the ratio $3:2$. Item A is sold at a profit of $20\%$. If the seller aims for an overall profit of $10\%$ on the total transaction, what must be the percentage profit or loss achieved on Item B?
Principal $P_1$ is invested at a simple interest rate of $R\%$ per annum for $T$ years. Principal $P_2 = 1.5 P_1$ is invested at a rate of $(R+2)\%$ per annum for $\frac{T}{2}$ years. If the total interest earned on $P_2$ is exactly $80\%$ of the total interest earned on $P_1$, determine the value of $R$.
A storage tank is initially $\frac{3}{5}$ full of water. $20\%$ of the water currently in the tank is then drained out. Following this, $\frac{1}{4}$ of the remaining water is added back into the tank. If the final amount of water in the tank is $360$ litres, what is the full capacity of the tank in litres?
Solution X is $15\%$ acid by volume, and Solution Y is $40\%$ acid by volume. A chemist mixes a volume of Solution X with $20$ litres of Solution Y to create a new mixture that is $25\%$ acid. How many litres of Solution X were used in the mixture?
If $\sqrt{x} - \frac{1}{\sqrt{x}} = 3$, what is the value of the expression $x^2 + \frac{1}{x^2}$?
Find the number of positive integers $k$ such that both linear inequalities are satisfied: $3k - 5 \ge 10$ and $4k + 1 \le 30$.
Given the formula $y = \frac{ax - b}{cx + d}$, express $x$ in terms of $y, a, b, c$, and $d$.
A sequence is defined by the explicit rule $T_n = \frac{n^3}{n^2 + 2n + 2}$. Determine the value of the 5th term, $T_5$.
If the function is defined by $f(x) = \frac{x}{x-1}$ and it is known that $f(k) = 2$, what is the value of $f(2k)$?
The solution to the linear equation $2(x-1) = 5x + 4$ represents the $x$-coordinate of the intersection point of which pair of simultaneous linear equations?
A pattern is formed by placing $n$ squares (side length 1 unit) side-by-side in a single straight row. What is the algebraic expression for the perimeter $P_n$ of this resulting figure?
The difference between the squares of any two consecutive positive odd integers is always divisible by which largest integer? (Hint: Let the consecutive odd integers be $2k-1$ and $2k+1$).
The line $L$ passes through the points $P(k, 1)$ and $Q(5, 7)$. If the gradient of line $L$ is $m=2$, determine the value of the parameter $k$.
A line is defined by the Standard Form equation $3x - \sqrt{2}y = 6$. Determine the slope ($m$) and the coordinates of the $y$-intercept ($B$).
Line $L_1$ passes through the points $A(-1, 5)$ and $B(3, 1)$. Line $L_2$ is the perpendicular bisector of the segment $AB$. Find the equation of line $L_2$.
A deep-sea submersible begins its ascent from a depth of $-4000$ meters below sea level. It rises at a constant vertical rate of $2$ meters per second. If $t$ is the time in seconds and $d$ is the depth (where $d=0$ is sea level), determine the amount of time, in minutes, required for the submersible to first reach a depth of $-400$ meters.
The line $L_1$ has a slope of $m_1 = 2$. The line $L_2$ is defined by the equation $Ax - 2y = 5$. If $L_1$ is parallel to $L_2$, determine the value of the parameter $A$.
Rationalise the denominator of the expression $X = \frac{\sqrt{2}}{\sqrt{3} + 1}$.
A right triangle has legs of length $4\sqrt{3}$ units and $2\sqrt{5}$ units. What is the length of the hypotenuse?
An equilateral triangle has a side length of $s = 6$ units. Find the exact length of its altitude $h$.
A rectangular prism has dimensions $3\sqrt{2}$, $\sqrt{7}$, and $5$. Calculate the length of the longest internal diagonal $D$.
Given a triangle where $\tan(\theta) = 1$, find the exact value of $\sin(\theta)$.
A square with side length $x$ has its area increased by $10$ units, resulting in a new area of $(27 + 12\sqrt{2})$ units. Find $x$.
An isosceles triangle has equal sides of length $6$ units and a base of length $4\sqrt{5}$ units. Calculate the area of the triangle.