📊 BUSINESS MATHEMATICS – SUMMARY NOTES
🧠 1. Meaning of Business Mathematics
Business Mathematics applies mathematical concepts to solve business and financial problems like profit, loss, interest, discount, and statistics.
👉 It helps in decision making, planning, and forecasting.
🧾 2. Ratio and Proportion
Ratio
Comparison of two quantities of the same kind.
Formula:
Ratio=ab or a:bRatio=ba or a:b
Proportion
Two ratios are equal.
If ab=cdba=dc, then a, b, c, d are in proportion.
Types:
- Direct proportion → both increase/decrease together
- Inverse proportion → one increases, other decreases
💰 3. Percentage
Percentage=ValueTotal Value×100Percentage=Total ValueValue×100
Example:
If marks = 80 out of 100 → 80100×100=80%10080×100=80%
💵 4. Profit, Loss & Discount
| Concept | Formula |
|---|---|
| Cost Price (CP) | Buying Price |
| Selling Price (SP) | Selling Price |
| Profit / Gain | SP − CP |
| Loss | CP − SP |
| Profit % | ProfitCP×100CPProfit×100 |
| Loss % | LossCP×100CPLoss×100 |
| Discount | Marked Price−Selling PriceMarked Price−Selling Price |
🏦 5. Simple Interest (SI)
SI=P×R×T100SI=100P×R×T
where
P = Principal, R = Rate (%), T = Time (years)
💹 6. Compound Interest (CI)
A=P(1+R100)TA=P(1+100R)TCI=A−PCI=A−P
If interest compounded half-yearly or quarterly:A=P(1+R/n100)nTA=P(1+100R/n)nT
where n = number of times interest compounded per year.
💱 7. Ratio Analysis in Business
| Ratio | Formula | Meaning |
|---|---|---|
| Current Ratio | Current Assets / Current Liabilities | Liquidity position |
| Debt-Equity Ratio | Debt / Equity | Financial stability |
| Gross Profit Ratio | (Gross Profit / Sales) × 100 | Profitability |
| Net Profit Ratio | (Net Profit / Sales) × 100 | Efficiency |
📉 8. Averages & Mean
Arithmetic Mean (A.M.)
A.M.=Sum of all observationsNo. of observationsA.M.=No. of observationsSum of all observations
Weighted Mean
Xˉ=Σ(w×x)ΣwXˉ=ΣwΣ(w×x)
📈 9. Simple Linear Equations
Used to solve unknown values in business problems.
Example:3x+2=11⇒x=33x+2=11⇒x=3
Simultaneous equations:2x+3y=12, x+2y=82x+3y=12,x+2y=8
Solve using elimination or substitution method.
📊 10. Ratio of Mixtures
If two types are mixed in ratio a:ba:b:Price of mixture=aP1+bP2a+bPrice of mixture=a+baP1+bP2
📆 11. Time, Work & Wages
| Concept | Formula |
|---|---|
| If A can do work in x days → 1 day’s work = 1/x | |
| If A & B work together → 1 day’s work = 1/x + 1/y | |
| Total time together → xyx+yx+yxy days |
🕒 12. Time & Distance
Speed=DistanceTime, Time=DistanceSpeedSpeed=TimeDistance,Time=SpeedDistance
Conversions
- 1 km = 1000 m
- 1 hour = 60 min = 3600 sec
Average Speed
Avg Speed=2xyx+y (when same distance)Avg Speed=x+y2xy (when same distance)
📉 13. Simple Series and Progressions
Arithmetic Progression (A.P.)
a,a+d,a+2d,a+3d…a,a+d,a+2d,a+3d…nth term=a+(n−1)dnth term=a+(n−1)dSum of n terms=n2[2a+(n−1)d]Sum of n terms=2n[2a+(n−1)d]
Geometric Progression (G.P.)
a,ar,ar2,ar3…a,ar,ar2,ar3…nth term=arn−1nth term=arn−1Sum of n terms=arn−1r−1Sum of n terms=ar−1rn−1
💹 14. Matrices & Determinants
Matrix
A rectangular arrangement of numbers in rows & columns.
Example:A=[1234]A=[1324]
Order of Matrix
Rows × Columns (e.g., 2×2)
Determinant (2×2)
∣A∣=ad−bc∣A∣=ad−bcA=[abcd]A=[acbd]
Applications
Used to solve simultaneous linear equations in business.
📊 15. Permutation and Combination
Permutation (Arrangement)
nPr=n!(n−r)!nPr=(n−r)!n!
Combination (Selection)
nCr=n!r!(n−r)!nCr=r!(n−r)!n!
💹 16. Probability (Basics)
P(E)=Favorable outcomesTotal outcomesP(E)=Total outcomesFavorable outcomes
Example:
If a coin is tossed,
P(Head) = 1/2, P(Tail) = 1/2.
Range: 0 ≤ P(E) ≤ 1
📉 17. Statistics in Business
| Measure | Formula | Purpose |
|---|---|---|
| Mean (Average) | Σx / n | Central value |
| Median | Middle value | Divides data equally |
| Mode | Most frequent value | Most common |
| Range | Max − Min | Spread of data |
| Standard Deviation (σ) | Σ(x−xˉ)2nnΣ(x−xˉ)2 | Measure of variation |
🧮 18. Simple Linear Regression
Used to find relationship between two variables (x, y).y=a+bxy=a+bx
where
b = regression coefficient = Σ(x−xˉ)(y−yˉ)Σ(x−xˉ)2Σ(x−xˉ)2Σ(x−xˉ)(y−yˉ)
💹 19. Present Value & Future Value
| Concept | Formula |
|---|---|
| Future Value (FV) | P(1+r100)nP(1+100r)n |
| Present Value (PV) | FV(1+r100)n(1+100r)nFV |
Used in investment decisions and annuities.
🧾 20. Logarithms (Basic Rules)
| Rule | Formula |
|---|---|
| Product | log(ab) = log a + log b |
| Quotient | log(a/b) = log a − log b |
| Power | log(aⁿ) = n log a |
| Base change | logₐb = log b / log a |
✅ 21. Business Applications
- Interest & investments → Banking & finance
- Cost & revenue analysis → Economics
- Depreciation & growth → Accounting
- Statistics & forecasting → Marketing, Management
🧩 22. Quick Formulas Recap
| Topic | Formula |
|---|---|
| Simple Interest | PRT100100PRT |
| Compound Interest | P(1+R100)T−PP(1+100R)T−P |
| Profit % | ProfitCP×100CPProfit×100 |
| Loss % | LossCP×100CPLoss×100 |
| Average | ΣxnnΣx |
| Speed | Distance / Time |
| A.P. nth term | a + (n−1)d |
| G.P. nth term | arⁿ⁻¹ |
| Permutation | nPr=n!(n−r)!nPr=(n−r)!n! |
| Combination | nCr=n!r!(n−r)!nCr=r!(n−r)!n! |