Di
Key Concepts & Formulas
Provide 5-7 essential concepts for Di (Data Interpretation):
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Percentage Calculation | (Part/Whole) × 100; Essential for pie charts and comparing values |
| 2 | Average/Ratio | Sum of values ÷ Number of values; Compare two quantities by division |
| 3 | Growth/Decline % | [(New-Old)/Old] × 100; Measures change over time periods |
| 4 | Speed-Distance-Time | Distance = Speed × Time; Often combined with DI in train problems |
| 5 | Pie Chart Angle | (Value/Total) × 360°; Converts data to degrees for pie charts |
| 6 | Table Reading | Row × Column intersection; Locate specific data points quickly |
10 Practice MCQs
Q1. A train travels 240 km in 4 hours. What is its average speed? A) 50 km/h B) 60 km/h C) 70 km/h D) 80 km/h
Answer: B) 60 km/h
Solution: Speed = Distance ÷ Time = 240 km ÷ 4 hours = 60 km/h
Shortcut: Direct division: 240 ÷ 4 = 60
Concept: Di - Basic speed calculation from tabular data
Q2. In a pie chart, if a sector represents 25% of total, what is its angle? A) 45° B) 60° C) 90° D) 120°
Answer: C) 90°
Solution: Angle = (Percentage/100) × 360° = (25/100) × 360° = 0.25 × 360° = 90°
Shortcut: 25% = 1/4, so 360° ÷ 4 = 90°
Concept: Di - Pie chart angle calculation
Q3. The table shows passengers: Mumbai-450, Delhi-380, Chennai-320. Total passengers? A) 1050 B) 1150 C) 1250 D) 1350
Answer: B) 1150
Solution: Total = 450 + 380 + 320 = 1150
Shortcut: Add hundreds first: 400+300+300=1000, then 50+80+20=150
Concept: Di - Table data summation
Q4. Railway ticket sales increased from 1200 to 1500. Find percentage increase. A) 20% B) 25% C) 30% D) 35%
Answer: B) 25%
Solution: Increase % = [(1500-1200)/1200] × 100 = (300/1200) × 100 = 0.25 × 100 = 25%
Shortcut: 300/1200 = 1/4 = 25%
Concept: Di - Percentage growth calculation
Q5. In a bar graph, train A's passengers = 800, train B's = 600. Ratio A:B? A) 3:4 B) 4:3 C) 2:3 D) 3:2
Answer: B) 4:3
Solution: Ratio = 800:600 = 8:6 = 4:3
Shortcut: Divide both by 200: 4:3
Concept: Di - Bar graph ratio interpretation
Q6. A train's average speed is 72 km/h. How many meters per second? A) 15 m/s B) 20 m/s C) 25 m/s D) 30 m/s
Answer: B) 20 m/s
Solution: 72 km/h = 72 × (1000/3600) m/s = 72 × (5/18) = 20 m/s
Shortcut: km/h to m/s: multiply by 5/18
Concept: Di - Unit conversion in speed problems
Q7. Pie chart shows: AC coaches 30%, Sleeper 45%, General 25%. If total coaches = 200, find Sleeper coaches. A) 80 B) 90 C) 100 D) 110
Answer: B) 90
Solution: Sleeper coaches = 45% of 200 = 0.45 × 200 = 90
Shortcut: 45% = 9/20, so 200 × 9/20 = 90
Concept: Di - Pie chart value extraction
Q8. Table shows monthly earnings: Jan-25000, Feb-28000, Mar-27000. Average monthly earning? A) 26000 B) 26500 C) 26667 D) 27000
Answer: C) 26667
Solution: Average = (25000+28000+27000) ÷ 3 = 80000 ÷ 3 = 26666.67 ≈ 26667
Shortcut: Add: 25+28+27=80, 80÷3=26.67
Concept: Di - Average from tabular data
Q9. Two trains have speed ratio 4:5. If slower train covers 240 km in 3 hours, find faster train's speed. A) 80 km/h B) 100 km/h C) 120 km/h D) 150 km/h
Answer: B) 100 km/h
Solution: Slower train speed = 240 ÷ 3 = 80 km/h Ratio 4:5 means 4 units = 80 km/h 1 unit = 20 km/h Faster train = 5 units = 5 × 20 = 100 km/h
Shortcut: 80 × (5/4) = 100
Concept: Di - Ratio application in speed problems
Q10. A train's journey time reduced from 6 hours to 5 hours. Find percentage time saving. A) 15.67% B) 16.67% C) 17.67% D) 18.67%
Answer: B) 16.67%
Solution: Saving % = [(6-5)/6] × 100 = (1/6) × 100 = 16.67%
Shortcut: 1/6 = 16.67% (memorize common fractions)
Concept: Di - Percentage reduction calculation
5 Previous Year Questions
PYQ 1. The pie chart shows railway station passenger distribution. If total passengers = 36000 and Chennai sector angle = 72°, find Chennai passengers. [RRB NTPC 2021 CBT-1]
Answer: 7200
Solution: 72° represents 72/360 = 1/5 of total Chennai passengers = 36000 × (1/5) = 7200
Exam Tip: Remember: 1° = Total/360, so multiply angle by (Total/360)
PYQ 2. Table shows train punctuality: Train A-85%, Train B-78%, Train C-92%. If each operated 50 trips, find total punctual trips. [RRB Group D 2022]
Answer: 127.5 ≈ 128 trips
Solution: Train A: 50 × 0.85 = 42.5 Train B: 50 × 0.78 = 39 Train C: 50 × 0.92 = 46 Total = 42.5 + 39 + 46 = 127.5
Exam Tip: Round only final answer, maintain decimals in intermediate steps
PYQ 3. Bar graph shows monthly ticket sales (in thousands): Apr-25, May-30, Jun-35, Jul-40. Find average monthly growth rate. [RRB ALP 2018]
Answer: 20%
Solution: Growth: Apr-May = (30-25)/25 = 20% May-Jun = (35-30)/30 = 16.67% Jun-Jul = (40-35)/35 = 14.29% Average = (20+16.67+14.29)/3 = 16.99% ≈ 17%
Exam Tip: Calculate individual growth rates first, then average them
PYQ 4. In a railway workshop, 40% workers are technicians, 35% are supervisors, rest are helpers. If helpers = 150, find total workers. [RRB JE 2019]
Answer: 600
Solution: Helpers % = 100 - 40 - 35 = 25% 25% = 150 workers 100% = 150 × 4 = 600 workers
Exam Tip: Find remaining percentage first, then use unitary method
PYQ 5. A train's passenger capacity utilization: Mon-65%, Tue-70%, Wed-75%, Thu-80%, Fri-85%. Find average utilization. [RPF SI 2019]
Answer: 75%
Solution: Average = (65+70+75+80+85) ÷ 5 = 375 ÷ 5 = 75%
Exam Tip: For evenly spaced numbers, middle value is the average
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| km/h to m/s | Multiply by 5/18 | 72 km/h = 72 × 5/18 = 20 m/s |
| Percentage to angle | Multiply by 3.6 | 25% = 25 × 3.6 = 90° |
| Finding 1% quickly | Divide by 100 | 1% of 4500 = 45 |
| Ratio simplification | Find HCF | 800:600 = 8:6 = 4:3 |
| Average of consecutive | Use middle value | 65,70,75,80,85 → avg = 75 |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Not reading units properly | Rush through questions | Always check km/h vs m/s, thousands vs lakhs |
| Calculating wrong base in % | Using new value as base | Always use original value as base: (Change/Original) × 100 |
| Rounding too early | Trying to save time | Keep full precision until final answer |
| Misreading table rows/columns | Poor visualization | Use finger to track, double-check intersection |
| Forgetting to convert units | Mixing km with meters | Always write units in calculations |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| 1% = ? degrees in pie chart | 3.6° |
| km/h to m/s conversion factor | 5/18 |
| Average formula | Sum ÷ Count |
| Growth % formula | [(New-Old)/Old] × 100 |
| 360° represents | 100% of data |
| Ratio 4:5 means | First is 80% of second |
| Speed × Time = | Distance |
| 45° in pie chart = | 12.5% of total |
| If 20% = 80, then 100% = | 400 |
| Consecutive numbers average | Middle value |
Topic Connections
Direct Link:
- Percentage calculations - Foundation for all DI problems
- Ratio & Proportion - Essential for comparing data sets
- Average - Central to analyzing trends in graphs
Combined Questions:
- DI + Speed-Distance-Time - Train schedules and average speeds
- DI + Percentage - Growth rates and market share analysis
- DI + Profit-Loss - Revenue and expense analysis in railway operations
Foundation For:
- Advanced Statistics - Standard deviation, correlation analysis
- Financial Mathematics - Revenue projections, budget analysis
- Operations Research - Optimizing train schedules and resource allocation
BETA
