📊 Quantitative Aptitude – Tables
(Manipur Patwari / Lekhpal – Study Notes)
Tables are systematic arrangements of numbers (or other data) in rows and columns that help you solve problems quickly.
They are especially useful for:
- Multiplication & Division (quick lookup)
- Rates, speeds, and work problems
- Unit conversion (time, distance, money, etc.)
- Probability & statistics (counts, frequencies)
- Progressions & series (listing terms)
1️⃣ Simple Explanation
-
What is a table?
A table is a grid of rows and columns where each cell contains a value that follows a logical rule. -
Why use tables?
- Speed: Once the table is set up, you can read off any required value instantly.
- Accuracy: Reduces mental calculation errors.
- Clarity: Visual representation of relationships (e.g., how many days a job takes with different workers).
-
Common types in exams
Type Typical Problem Example Multiplication / Division “Find 7 × 6” 7 × 6 = 42 Time & Work “5 men finish a work in 8 days” Table of days vs. men Rate / Speed “A train covers 120 km in 2 hrs” Speed = 60 km/h Unit Conversion “Convert 150 kg to lb” 150 kg × 2.20462 = 330.69 lb Probability “Probability of rolling a 4” Count of favourable outcomes / total outcomes Progression “Find the 8th term of 3,6,9,…” 3 × 8 = 24
2️⃣ Key Points (What to Remember)
| Point | Detail |
|---|---|
| 1. Create the table first | Write the independent variable (e.g., days, workers) in the first column. |
| 2. Use a consistent rule | Each cell is derived from a simple operation (multiply or divide). |
| 3. Keep it clean | Use clear headings and avoid clutter. |
| 4. Check for symmetry | In multiplication tables, the table is symmetric; use that to double‑check. |
| 5. Use “two‑way” tables | For rate problems, list both speed and time in separate columns for quick cross‑checking. |
| 6. Leverage “inverse” relationships | If A × B = C, then B = C ÷ A. Use this to fill missing values. |
| 7. Remember “proportionality” | If A workers finish X days, then kA workers finish X/k days (if work is proportional). |
| 8. Use “unit rate” | Convert complex rates to a simple “per unit” value first (e.g., per hour, per kg). |
| 9. Check for integer solutions | Tables often show integer values; if you get a fraction, re‑check assumptions. |
| 10. Practice with real data | Create tables for daily expenses, rainfall, etc., to get comfortable. |
3️⃣ Worked Example
Problem:
The construction of a road section takes 12 days when 7 workers are employed. How many days will it take 10 workers to complete the same section, assuming all workers work at the same rate?
Step‑by‑Step Using a Table
| Workers (W) | Days (D) | Work Done (W × D) |
|---|---|---|
| 7 | 12 | 84 |
| 8 | ? | 84 |
| 9 | ? | 84 |
| 10 | ? | 84 |
Why this works:
Total work = Workers × Days (constant).
So, for each new worker count, we solve for days:
- For 8 workers:
( D = \frac{84}{8} = 10.5 ) days - For 9 workers:
( D = \frac{84}{9} \approx 9.33 ) days - For 10 workers:
( D = \frac{84}{10} = 8.4 ) days
Answer:
It will take 8.4 days for 10 workers to finish the road section.
Quick Check (Inverse Relationship)
- Work done per day by 7 workers: ( \frac{84}{12} = 7 ) units/day
- Work per day by 10 workers: ( 10 ) units/day
- Days needed: ( \frac{84}{10} = 8.4 ) days ✔️
4️⃣ Quick Revision Summary
| Topic | What to Know | Tip |
|---|---|---|
| Multiplication Tables | 1–12 (or 1–20) | Memorize up to 12 for speed; use symmetry. |
| Division Tables | 1 ÷ 2 to 12 ÷ 12 | Look at multiplication table backwards. |
| Time & Work | Work = Workers × Days | Build a table; keep |