The Market
Ratio, Percentage, Interest & Financial Arithmetic
The Human Problem
The number system now leaves the abstract page and enters civilization's marketplace. A merchant does not merely ask "How much?" They ask: "How much compared with what?", "At what rate?", and "What will it become over time?"
QUANTITY →
COMPARISON →
RATIO →
PROPORTION →
RATE →
PERCENTAGE →
PRICE →
PROFIT / LOSS →
DISCOUNT / TAX →
INTEREST →
GROWTH
The 40 Commercial Cells
Mathematics of Scaling, Change & Value
CELL 01
The Idea of Ratio
:
- Comparing quantities
- Notation (a : b)
- Part-to-part vs Part-to-whole
CELL 02
Simplifying Ratios
18:24
→
3:4
- Dividing by HCF
- Simplest form
- Connecting to fractions
CELL 03
Equivalent Ratios
3:5
=
6:10
=
30:50
- Scaling up/down
- Same relationship
- Multiplier principle (ka:kb)
CELL 04
Sharing in a Ratio
3
5
- Dividing a total quantity
- Finding total parts
- Value of one part
CELL 05
Proportion
x5
=
1215
- Equality of two ratios
- Cross multiplication
- Finding a missing term
CELL 06
Unitary Method
5 items₹100
↓
1 item₹20
↓
8 items₹160
- Find value of one unit
- Scale to required quantity
- Foundation for word problems
CELL 07
Direct Proportion
- Quantities scale together
- y ∝ x (y = kx)
- Constant ratio
CELL 08
Inverse Proportion
- Opposite scaling
- y ∝ 1/x (xy = k)
- Constant product (e.g., Speed/Time)
CELL 09
Rate & Unit Rate
60km/h
→
- Comparing different units
- Speed, price rate, productivity
- Bridge to Physics
CELL 10
Percentage
%
- "Per hundred" (1/100)
- Fraction ↔ Decimal ↔ %
- Universal scaling metric
CELL 11
Finding Percentages
20% of 200
= 40
- Part as % of whole
- % of a quantity
- Finding whole from %
CELL 12
Percentage Increase
↑
- (Increase / Original) × 100
- Growth measurement
- Denominator is original value
CELL 13
Percentage Decrease
↓
- (Decrease / Original) × 100
- Reduction measurement
- Depreciation preview
CELL 14
Successive Changes
100 →
+20% →
120 →
-20% →
96
- Changes compound
- +20% then -20% ≠ 0 change
- Net effect calculation
CELL 15
Marked Price
₹1000
- Displayed/List price
- Base for discount calculation
- Not always selling price
CELL 16
Discount
-10%
OFF MP
- Discount = MP - SP
- Discount % = (Disc/MP) × 100
- Successive discounts
CELL 17
Cost Price (CP)
CP
IN
- Acquisition/Production cost
- Base for Profit/Loss %
- Initial investment
CELL 18
Selling Price (SP)
SP
OUT
- Final transaction value
- SP = CP + Profit (or - Loss)
- SP = MP - Discount
CELL 19
Profit
- Occurs when SP > CP
- Profit = SP - CP
- Profit % = (Profit/CP) × 100
CELL 20
Loss
- Occurs when SP < CP
- Loss = CP - SP
- Loss % = (Loss/CP) × 100
CELL 21
Reverse Calculations
SP
÷ (1±p)
CP
- Finding CP given SP & %
- Algebraic rearrangement
- Formula-based commerce
CELL 22
Markup
↑
- Increase from CP to MP
- Markup = MP - CP
- Distinct from profit
CELL 23
Taxes
₹100 + 18% GST = ₹118
- Sales tax / GST
- Calculated on selling price
- Inclusive vs Exclusive
CELL 24
Commission
4%
- Percentage of sales value
- Agent/Broker compensation
- Proportional reward
CELL 25
Simple Interest
SI =
P×R×T
100
- Interest on principal only
- Linear growth model
- Amount = P + SI
CELL 26
Rearranging Variables
P = 100I / RT
R = 100I / PT
T = 100I / PR
- Solving for unknowns
- Algebraic manipulation
- Equation flexibility
CELL 27
Compound Interest
- Interest earns interest
- A = P(1 + R/100)ⁿ
- Exponential growth model
CELL 28
Compounding Frequency
Annualn=1
Half-Yearn=2
Quarterlyn=4
Monthlyn=12
- Periods per year (m)
- Adjusting Rate (R/m)
- Adjusting Time (T×m)
CELL 29
Depreciation
- Loss of value over time
- V = P(1 - R/100)ⁿ
- Reverse of compound growth
CELL 30
General Growth
- Population, Bacteria, Inflation
- Compound formula applications
- Bridge to exponential functions
CELL 31
Installments & EMI
- Down payment & Loan
- Equated Monthly Installment
- Amortization preview
CELL 32
Currency & Exchange
$ ↔ ₹
- Exchange rates
- Proportional conversion
- Global trade arithmetic
CELL 33
Mixtures & Alligation
- Mixing prices/concentrations
- Weighted reasoning
- Advanced problem solving
CELL 34
Weighted Average
- Basic arithmetic mean
- Values with different weights
- Portfolio/Grade calculations
CELL 35
Unit Economics
REV / UNIT
- COST / UNIT
= PROFIT
- Analyzing per-item metrics
- Scaling up operations
- Bridge to Business Economics
CELL 36
Break-Even Preview
- Fixed vs Variable costs
- Point of zero profit/loss
- Intersection of Revenue/Cost
CELL 37
Market Word Problems
COST → MARKUP → DISC
↓
FINAL PROFIT %
- Multi-step commercial logic
- Tracking changing values
- Mathematical simulation
CELL 38
Mathematics of Rates
partwhole
disttime
moneytime
profitcost
- Unifying ratio structures
- Universal application
- Cross-disciplinary concept
CELL 39
Representation Switching
- Fluidity between forms
- 25% ↔ 0.25 ↔ 1/4
- Choosing optimal format
CELL 40
The Market as a System
- Synthesis of all concepts
- Scaling, change, and value
- Foundation for Economics
Exit Portal
After humans learned to calculate known quantities, civilization reached the next great question: What if the quantity we need is unknown? The unknown gets a symbol. That is the birth of Algebra.