Business Mathematics means using basic mathematics to solve day-to-day business and commerce calculations—pricing, discounts, taxes, commissions, profit planning, and interpreting numbers correctly.
Why it matters (exam points):
A ratio compares two quantities of the same kind.
Types of ratios:
Simplification rule: Divide both terms by their HCF.
Quick example: If salaries are ₹36,000 and ₹54,000 then ratio = 36,000:54,000 = 2:3.
When two ratios are equal, we say they are in proportion:
If sales are directly proportional to advertising spend, then spend doubles → sales (expected) doubles.
Example: If 10 salespeople sell 500 units, then 15 salespeople sell: 500 × (15/10) = 750 units (assuming same efficiency).
If work is fixed, more workers mean less time.
Example: 12 workers finish in 10 days. 15 workers finish in: 10 × (12/15) = 8 days.
Percentage means “per hundred”.
Core conversions:
Access the complete note and unlock all topic-wise content
It's free and takes just 5 seconds
From this topic
Direct proportion (direct variation): Two quantities are in direct proportion when they change in the same direction.
Example (business): If sales are proportional to advertising (other things constant), then increasing advertising from 10 units to 15 units changes sales by the factor 15/10.
Inverse proportion (inverse variation): Two quantities are in inverse proportion when one increases and the other decreases such that their product remains constant.
Example (work-time): 12 workers finish a job in 10 days. Days for 15 workers = 10 × (12/15) = 8 days (same efficiency).
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.
Business Mathematics means using basic mathematics to solve day-to-day business and commerce calculations—pricing, discounts, taxes, commissions, profit planning, and interpreting numbers correctly.
Why it matters (exam points):
A ratio compares two quantities of the same kind.
Types of ratios:
Simplification rule: Divide both terms by their HCF.
Quick example: If salaries are ₹36,000 and ₹54,000 then ratio = 36,000:54,000 = 2:3.
When two ratios are equal, we say they are in proportion:
If sales are directly proportional to advertising spend, then spend doubles → sales (expected) doubles.
Example: If 10 salespeople sell 500 units, then 15 salespeople sell: 500 × (15/10) = 750 units (assuming same efficiency).
If work is fixed, more workers mean less time.
Example: 12 workers finish in 10 days. 15 workers finish in: 10 × (12/15) = 8 days.
Percentage means “per hundred”.
Core conversions:
Important formulas (exam-ready):
Example (successive discount): 20% then 10% → net discount = 20 + 10 − (20×10)/100 = 28%.
An average represents the central value.
Mean = (Sum of observations) / (Number of observations)
Used for routine business data (daily sales, expenses).
Weighted mean = Σ(wx) / Σw
Used when quantities have different importance (price with quantities, marks with credits).
Example: Prices ₹10 (100 units), ₹12 (50 units) → average price = (10×100 + 12×50)/150 = 10.67 (approx).
These are the most asked calculations in commerce papers.
Flow (typical pricing chain):
If 15% of N = 300, then N = 300 × (100/15).
Use: (a/b)×100. Reduce fraction first.
Average = (n1×x1 + n2×x2)/(n1+n2)
Divide total T in ratio a:b:c → (a/(a+b+c))T, (b/(a+b+c))T, (c/(a+b+c))T.
Pseudo-steps for a typical % word problem:
1) Identify the base quantity (Old value / Marked price / Cost price).
2) Convert the percentage to a multiplier (e.g., +20% => ×1.20, -15% => ×0.85).
3) Apply in correct order (successive changes multiply).
4) Round only at the end (keep fractions during working).
If these notes helped you, a quick review supports the project and helps more students find it.
Percentage change shows how much a value has increased or decreased relative to the old value.
Formula: % change = ((New − Old) / Old) × 100
Example: Value changes from 500 to 650. Increase = 650 − 500 = 150 % increase = (150/500) × 100 = 30%
So, the value increases by 30%.
A ratio is a comparison of two like quantities expressed as a:b. Example: Profit ₹20,000 and sales ₹1,00,000 ⇒ profit:sales = 20,000:1,00,000 = 1:5.
A proportion is an equality of two ratios. If a:b = c:d, then a×d = b×c.
Conclusion: Ratio and proportion give a simple, accurate way to compare quantities and make business decisions using numbers.