Arithmetic
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ARITHMETIC
Ratios and Proportions
| Concept | Key Idea | Example |
|---|---|---|
| Ratio | Comparison of two quantities of same kind | 2 : 3 |
| Direct Proportion | Both increase/decrease together | More workers → More work done |
| Inverse Proportion | One increases, other decreases | More speed → Less time |
- Ratio = Quantity A : Quantity B
- In proportion: a : b = c : d → ad = bc
- Direct Proportion: A ↑ → B ↑
- Inverse Proportion: A ↑ → B ↓
Memory Box
“Cross multiply to check proportion → Product of extremes = Product of means”
“Cross multiply to check proportion → Product of extremes = Product of means”
Tip Box
Convert quantities into same units before forming ratios.
Convert quantities into same units before forming ratios.
Percentage and Its Applications
| Concept | Formula | Application |
|---|---|---|
| Percentage | (Value / Total) × 100 | Marks calculation |
| Profit | S.P − C.P | Shopkeeper profit |
| Loss | C.P − S.P | Discount sales |
| Discount | Marked Price − Selling Price | Festive offers |
| GST | (GST % × Price) / 100 | Billing in shops |
- Percentage = Per 100 value
- Profit % = (Profit / CP) × 100
- Loss % = (Loss / CP) × 100
- Discount % = (Discount / Marked Price) × 100
- GST = Added tax on goods & services
Memory Box
“CP → Cost Price
SP → Selling Price
MP → Marked Price”
“CP → Cost Price
SP → Selling Price
MP → Marked Price”
Tip Box
Always apply GST after discount, not before.
Always apply GST after discount, not before.
Interest (Simple & Compound)
| Type | Formula | Explanation |
|---|---|---|
| Simple Interest | SI = (P × R × T) / 100 | Interest only on principal |
| Compound Interest | A = P (1 + R/100)T | Interest on interest |
- P = Principal
- R = Rate of Interest
- T = Time
- CI is always greater than SI for same values
Memory Box
Simple Interest = Straight line growth
Compound Interest = Growing like tree branches
Simple Interest = Straight line growth
Compound Interest = Growing like tree branches
Tip Box
If compounding is yearly, use full formula once per year.
If compounding is yearly, use full formula once per year.
Simplification (BODMAS Rule)
| Order | Full Form |
|---|---|
| B | Brackets |
| O | Orders (Powers / Roots) |
| D | Division |
| M | Multiplication |
| A | Addition |
| S | Subtraction |
- Always solve within brackets first
- Division and Multiplication from left to right
- Addition and Subtraction from left to right
Memory Box
“BODMAS = Bracket Of Division Multiplication Addition Subtraction”
“BODMAS = Bracket Of Division Multiplication Addition Subtraction”
Tip Box
Never change order of operations even if result seems simple.
Never change order of operations even if result seems simple.