Arithmetic
ARITHMETIC
BODMAS Rule
| Order | Operation | Meaning | Example |
|---|---|---|---|
| B | Brackets | Operations inside ( ) first | (6+4) × 2 = 20 |
| O | Orders | Powers / Square roots | 2² = 4 |
| D | Division | Next priority | 20 ÷ 5 = 4 |
| M | Multiplication | Next priority | 4 × 3 = 12 |
| A | Addition | Then add | 5 + 2 = 7 |
| S | Subtraction | Last priority | 9 − 3 = 6 |
BODMAS Rule Order → Brackets → Orders → Division → Multiplication → Addition → Subtraction
If division and multiplication appear together, solve from left to right.
Ratios and Proportions
| Concept | Meaning | Example |
|---|---|---|
| Ratio | Comparison of two quantities | 2 : 3 |
| Proportion | Equality of two ratios | 2:3 = 4:6 |
| Direct Proportion | Both increase/decrease together | Wages ∝ Work done |
| Inverse Proportion | One increases, other decreases | Speed ∝ 1/Time |
| Comparison Type | Formula |
|---|---|
| Direct Proportion | x₁ / x₂ = y₁ / y₂ |
| Inverse Proportion | x₁ × y₁ = x₂ × y₂ |
Proportion property: If a : b = c : d → ad = bc
In exam problems, always convert different units into same units before comparing.
Profit, Loss and Discount
| Term | Formula |
|---|---|
| Profit | SP − CP |
| Loss | CP − SP |
| Profit % | (Profit / CP) × 100 |
| Loss % | (Loss / CP) × 100 |
| Discount | Marked Price − Selling Price |
| Discount % | (Discount / Marked Price) × 100 |
| Situation | Example |
|---|---|
| Profit Case | CP = ₹100, SP = ₹120 → Profit = ₹20 |
| Loss Case | CP = ₹80, SP = ₹70 → Loss = ₹10 |
| Discount Case | MP = ₹500, SP = ₹450 → Discount = ₹50 |
Profit/Loss is always calculated on Cost Price, not Selling Price.
Most competitive exams combine Discount with successive profit/loss questions. Be careful with percentage change.
Taxation (Sales Tax, VAT, GST)
| Tax Type | Meaning | Example |
|---|---|---|
| Sales Tax | Tax on goods sold | Used earlier before GST |
| VAT | Tax at each production stage | State-level tax earlier |
| GST | Single indirect tax in India | CGST + SGST / IGST |
| Formula | Usage |
|---|---|
| GST Amount = (GST% × Price) / 100 | To calculate tax amount |
| Final Price = Original Price + GST | Final payable amount |
GST full form → Goods and Services Tax (Introduced in India: 1 July 2017)
In exam numericals, always calculate GST separately, not included in cost price initially.
Simple Interest
| Formula | Meaning |
|---|---|
| SI = (P × R × T) / 100 | Simple Interest |
| Amount = P + SI | Total after interest |
| Symbol | Meaning |
|---|---|
| P | Principal |
| R | Rate per annum |
| T | Time (in years) |
Simple Interest increases linearly with time.
Always convert months into years in exams: 6 months = 0.5 years.
Compound Interest
| Formula | Usage |
|---|---|
| A = P(1 + R/100)ⁿ | Final Amount |
| CI = A − P | Compound Interest |
| Difference | Simple Interest | Compound Interest |
|---|---|---|
| Interest Base | Only on Principal | On Principal + Interest |
| Growth | Linear | Exponential |
Compound Interest > Simple Interest for same P, R, T (except for 1 year)
For 2 years: CI − SI = (P × R²)/10000