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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In business, every transaction finally answers one question: Did we gain (profit) or lose (loss)? This unit teaches the language of pricing and selling:
These topics appear repeatedly in B.Com/BBA and in B.Tech management/entrepreneurship papers because they connect directly to billing, quotations, retail pricing, and cost-volume-profit decisions.
Always check the base:
Mark-up is usually on cost:
If CP = 800 and profit = 25% on CP, SP = CP × (1 + 25/100) = 800 × 1.25 = 1000.
If SP = 1200 and profit = 20% on CP, SP = CP × 1.20 ⇒ CP = 1200/1.20 = 1000.
If CP = 1500 and SP = 1800, Profit = 300, Profit % = (300/1500)×100 = 20%.
This is a frequent confusion in exams.
Profit % = (Profit/CP)×100. Example: CP 100, profit 20% ⇒ profit 20, SP 120.
Profit % = (Profit/SP)×100. Example: SP 120, profit 20% on SP ⇒ profit = 0.20×120 = 24, CP = 96.
Important: The same number “20% profit” can mean different CP/SP depending on the base.
Conversion formulas:
(You don’t need to memorize if you can do a quick 100-base example.)
A reduction on list price given to retailers/wholesalers. Usually shown on invoice as deduction from MP.
Discount for early payment (credit terms).
If discounts are d1% and d2% successively: SP = MP × (1 − d1/100) × (1 − d2/100)
Net discount formula (two discounts): Net discount % = d1 + d2 − (d1×d2)/100
Example: 30% and 10% successive discount: Net discount = 30 + 10 − 3 = 37%.
Mark-up is usually computed on cost.
Margin (often called gross margin) is profit as a percentage of selling price.
Let mark-up = m% on CP. Then SP = CP × (1 + m/100). Margin on SP becomes: Margin % = [m / (100 + m)] × 100
Example: Mark-up 25% on cost ⇒ margin = 25/125 × 100 = 20%.
Break-even analysis answers: How much must we sell so that profit is zero?
BEP (units) = Fixed Cost / Contribution per unit
If contribution ratio is known:
Suppose:
SP = CP × (1 + p/100)
SP = CP × (1 − l/100)
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In business, every transaction finally answers one question: Did we gain (profit) or lose (loss)? This unit teaches the language of pricing and selling:
These topics appear repeatedly in B.Com/BBA and in B.Tech management/entrepreneurship papers because they connect directly to billing, quotations, retail pricing, and cost-volume-profit decisions.
Always check the base:
Mark-up is usually on cost:
If CP = 800 and profit = 25% on CP, SP = CP × (1 + 25/100) = 800 × 1.25 = 1000.
If SP = 1200 and profit = 20% on CP, SP = CP × 1.20 ⇒ CP = 1200/1.20 = 1000.
If CP = 1500 and SP = 1800, Profit = 300, Profit % = (300/1500)×100 = 20%.
This is a frequent confusion in exams.
Profit % = (Profit/CP)×100. Example: CP 100, profit 20% ⇒ profit 20, SP 120.
Profit % = (Profit/SP)×100. Example: SP 120, profit 20% on SP ⇒ profit = 0.20×120 = 24, CP = 96.
Important: The same number “20% profit” can mean different CP/SP depending on the base.
Conversion formulas:
(You don’t need to memorize if you can do a quick 100-base example.)
A reduction on list price given to retailers/wholesalers. Usually shown on invoice as deduction from MP.
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Trade discount:
Cash discount:
Successive discounts mean two or more discounts applied one after another on the reduced price (not added directly).
For two discounts d1% and d2%: Net discount % = d1 + d2 − (d1×d2)/100
Here d1 = 30 and d2 = 10: Net discount % = 30 + 10 − (30×10)/100 = 40 − 3 = 37%.
So, 30% and 10% successive discounts are equivalent to a single discount of 37%.
Profit % (generally on CP) = (Profit/CP) × 100
Example: CP = ₹1000, SP = ₹1200 Profit = 1200 − 1000 = ₹200 Profit % = (200/1000) × 100 = 20%
Loss % (generally on CP) = (Loss/CP) × 100
Example: CP = ₹1000, SP = ₹900 Loss = 1000 − 900 = ₹100 Loss % = (100/1000) × 100 = 10%
Conclusion: Profit/loss indicates gain or sacrifice in a transaction and percentage form helps compare performance across products or time.