Business mathematics are mathematics used by commercial enterprises to record and manage business operations. Commercial organizations use mathematics in accounting, inventory management, marketing, sales forecasting, and financial analysis.
Download this note as PDF at no cost
If any AD appears on download click please wait for 30sec till it gets completed and then close it, you will be redirected to pdf/ppt notes page.
Algebra helps convert business statements into mathematical form so we can solve for unknowns like price, quantity, cost, profit, demand, and break-even level.
Typical exam uses:
A linear equation in one variable has the form: ax + b = 0 (a ≠ 0)
Solution idea: isolate x.
Example: 3x + 15 = 0 ⇒ 3x = −15 ⇒ x = −5
A linear equation in two variables: ax + by = c.
To find unique values of x and y, we need two independent equations.
Example: 2x + y = 11 x + y = 7 Subtract second from first: x = 4, then y = 3.
If 2 notebooks + 1 pen cost ₹110 and 1 notebook + 1 pen costs ₹70: 2N + P = 110 N + P = 70 Subtract → N = 40, then P = 30.
A quadratic equation has the form: ax^2 + bx + c = 0 (a ≠ 0)
Quadratic formula: x = [−b ± √(b^2 − 4ac)] / (2a)
Discriminant (D): D = b^2 − 4ac
Quadratics occur when revenue/cost relationships create curved functions (e.g., profit with non-linear demand). Often we reject negative/irrational roots if not meaningful.
An inequality represents a range of possible values.
Examples:
Constraints like:
These are written using inequalities.
Break-even means profit = 0. So R = C. If R = pQ and C = F + vQ: pQ = F + vQ ⇒ (p − v)Q = F ⇒ Q = F/(p − v)
This is the same break-even logic you studied earlier, now expressed as algebra.
Many word problems reduce to linear equations after defining variables.
Steps (exam-friendly):
Common patterns:
Tip: After solving, substitute back into the original equation(s) to confirm.
Get instant access to notes, practice questions, and more benefits with our mobile app.
Algebra helps convert business statements into mathematical form so we can solve for unknowns like price, quantity, cost, profit, demand, and break-even level.
Typical exam uses:
A linear equation in one variable has the form: ax + b = 0 (a ≠ 0)
Solution idea: isolate x.
Example: 3x + 15 = 0 ⇒ 3x = −15 ⇒ x = −5
A linear equation in two variables: ax + by = c.
To find unique values of x and y, we need two independent equations.
Example: 2x + y = 11 x + y = 7 Subtract second from first: x = 4, then y = 3.
If 2 notebooks + 1 pen cost ₹110 and 1 notebook + 1 pen costs ₹70: 2N + P = 110 N + P = 70 Subtract → N = 40, then P = 30.
A quadratic equation has the form: ax^2 + bx + c = 0 (a ≠ 0)
Access the complete note and unlock all topic-wise content
It's free and takes just 5 seconds
From this topic
5x − 3 = 22 ⇒ 5x = 25 ⇒ x = 5. So, x = 5.
To solve simultaneous linear equations, we can use elimination.
Example: 2x + y = 11 x + y = 7
Subtract the second equation from the first: (2x + y) − (x + y) = 11 − 7 x = 4
Substitute x = 4 into x + y = 7: 4 + y = 7 ⇒ y = 3
Therefore, the solution is x = 4 and y = 3.
Break-even point is the level of sales/output at which profit is zero.
Profit Π = Revenue − Cost. At break-even, Π = 0, so Revenue = Cost.
If revenue R = pQ and cost C = F + vQ (fixed + variable), then: pQ = F + vQ (p − v)Q = F Q = F/(p − v)
This shows break-even units depend on fixed cost and contribution per unit (p−v).