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:
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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.
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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).
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).
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.