📚 Study Notes – “Tables” in Quantitative Aptitude
(JEST / IIT‑JEE – Competitive‑Exam Focused)
Why Tables?
Tables are the backbone of many aptitude problems. They compress information into a structured format, enabling quick pattern spotting, proportion solving, and the use of algebraic tricks. Mastery of tables turns a seemingly messy problem into a clean, linear equation.
1. Classifying Tables
| Type | Typical Data | Key Idea |
|---|---|---|
| Ratio Tables | Two columns of numbers that are in proportion | Cross‑multiplication, reduced fractions |
| Percentage Tables | Change in quantity expressed in percent | ( \text{Percent change} = \frac{\text{New} - \text{Old}}{\text{Old}}\times100 ) |
| Profit‑Loss Tables | Selling price, cost price, profit, loss | ( P = C+ \frac{C\cdot \text{Profit%}}{100} ) |
| Interest Tables | Principal, rate, time, SI, CI | ( SI = \frac{PRT}{100} ), ( CI = P\left[(1+\frac{R}{100})^T-1\right] ) |
| Speed–Time–Distance Tables | Time, speed, distance | ( D = \frac{T\cdot S}{60} ) (for km/min) |
| Weighted‑Average Tables | Quantity & Unit price | ( \text{Total cost} = \sum Q_i \times P_i ) |
| Discount / Mark‑up Tables | Marked price, discount, selling price | ( SP = MP(1-\frac{D}{100}) ) |
Tip: Always read the table top‑to‑bottom. The first row/column usually sets a base (e.g., “When speed = 60 km/hr”) from which all others are derived.
2. General Strategies
| Step | What to Do | Why It Helps |
|---|---|---|
| 1. Identify the unknowns | Write them down with variables | Keeps your focus on what’s missing |
| 2. Convert units | E.g., 1 hour = 60 min | Prevents unit‑confusion errors |
| 3. Use proportions | ( \frac{a}{b} = \frac{c}{d} ) | Handles ratio tables instantly |
| 4. Cross‑check with sums | Verify if the sum matches the total | Catch mistakes early |
| 5. Apply algebraic manipulation | Simplify fractions, isolate variables | Turns a multi‑step problem into one equation |
| 6. Check for “negative” percentages | If new value < old value | Avoids sign errors |
3. Detailed Derivations & Formulae
3.1 Ratio Tables
Suppose we have two columns (A) and (B) in proportion.
[ \frac{A}{B} = \frac{C}{D} ]
Derivation of Cross‑Multiplication
[ A\cdot D = B\cdot C ;\Rightarrow; C = \frac{A\cdot D}{B} ]
Use this when one value is missing but the others are known.
3.2 Percentage Change
If a quantity changes from (X) to (Y):
[ \text{Percent change} = \frac{Y-X}{X}\times 100 % ]
- Increase: (Y > X) → positive percent
- Decrease: (Y < X) → negative percent
3.3 Profit & Loss
Let (C) be cost price and (SP) be selling price.
[ \text{Profit} = SP - C ] [ \text{Profit%} = \frac{SP-C}{C}\times100 ] [ SP = C\left(1+\frac{\text{Profit%}}{100}\right) ]
Loss is treated similarly with a minus sign.
3.4 Simple Interest (SI)
[ SI = \frac{P \times R \times T}{100} ]
- (P) = principal
- (R) = annual rate (%)
- (T) = time (years)
3.5 Compound Interest (CI)
[ CI = P\left[(1+\frac{R}{100})^T - 1\right] ]
Derivation:
After 1 year: (P_1 = P(1+\frac{R}{100}))
After 2 years: (P_2 = P_1(1+\frac{R}{100}))
Continue to (T) years → geometric progression.
3.6 Speed–Time–Distance
[ D = \frac{T \times S}{60} ]
(If (S) is in km/hr and (T) in minutes.)
Derivation
(1;\text{hr}=60;\text{min}) → (S;\text{km/h} = \frac{S}{60};\text{km/min}).
Distance (D = \text{speed} \times \text{time}).
3.7 Weighted Average
If you buy (q_i) units at price (p_i) each:
[ \text{Total cost} = \sum_{i=1}^{n} q_i p_i \