Shortcut Techniques
Key Concepts & Formulas
Provide 5-7 essential concepts for Shortcut Techniques:
| # | Concept | Quick Explanation |
|---|---|---|
| 1 | Digit Sum Method | Sum digits repeatedly until single digit; useful for quick divisibility checks and answer verification |
| 2 | Unit Digit Pattern | Focus only on unit digits for multiplication/division; saves time in complex calculations |
| 3 | Percentage as Fractions | Convert percentages to simple fractions (25% = 1/4, 12.5% = 1/8) for faster calculation |
| 4 | Ratio & Proportion Shortcuts | Use cross-multiplication and common factors to simplify ratio problems quickly |
| 5 | Speed-Distance-Time Tricks | Remember: If distance constant, speed ∝ 1/time; use relative speed concept for train problems |
| 6 | Approximation Technique | Round numbers to nearest 10/100, calculate, then adjust for exact answer |
| 7 | Digital Root for Verification | Sum of digits (digital root) of answer should match digital root of calculation |
10 Practice MCQs
Q1. A train travels 120 km in 2 hours. What is its speed in m/s? A) 15.67 m/s B) 16.67 m/s C) 18.67 m/s D) 20 m/s
Answer: B) 16.67 m/s
Solution: Speed = Distance/Time = 120 km/2 hours = 60 km/h Convert to m/s: 60 × (1000/3600) = 60 × (5/18) = 300/18 = 16.67 m/s
Shortcut: To convert km/h to m/s, multiply by 5/18 60 × 5/18 = 16.67 m/s
Concept: Shortcut Techniques - Unit conversion shortcuts
Q2. What is 15% of 240? A) 32 B) 36 C) 38 D) 42
Answer: B) 36
Solution: 15% = 10% + 5% 10% of 240 = 24 5% of 240 = 12 Total = 24 + 12 = 36
Shortcut: Break percentage into easy parts (10% + 5%)
Concept: Shortcut Techniques - Percentage decomposition
Q3. If a train of length 200m crosses a pole in 10 seconds, what is its speed? A) 20 m/s B) 72 km/h C) Both A & B D) Neither
Answer: C) Both A & B
Solution: Speed = Distance/Time = 200m/10s = 20 m/s Convert to km/h: 20 × (18/5) = 72 km/h
Shortcut: Remember 1 m/s = 3.6 km/h
Concept: Shortcut Techniques - Train problems basics
Q4. A railway ticket costs ₹450. If price increases by 20%, then decreases by 20%, what is the final price? A) ₹432 B) ₹450 C) ₹465 D) ₹420
Answer: A) ₹432
Solution: After 20% increase: 450 × 1.2 = ₹540 After 20% decrease: 540 × 0.8 = ₹432
Shortcut: Net effect = -4% (20 - 20 - 20×20/100 = -4%) 450 × 0.96 = ₹432
Concept: Shortcut Techniques - Successive percentage changes
Q5. Two trains of length 180m and 220m run in opposite directions at 50 km/h and 40 km/h. When will they cross each other? A) 14.4 sec B) 16 sec C) 18 sec D) 20 sec
Answer: B) 16 sec
Solution: Total distance = 180 + 220 = 400m Relative speed = 50 + 40 = 90 km/h = 90 × (5/18) = 25 m/s Time = 400/25 = 16 seconds
Shortcut: Opposite direction: add speeds; Same direction: subtract speeds
Concept: Shortcut Techniques - Relative speed in train problems
Q6. A train covers 600 km. If speed increases by 20 km/h, time reduces by 2 hours. Find original speed. A) 40 km/h B) 60 km/h C) 80 km/h D) 100 km/h
Answer: B) 60 km/h
Solution: Let original speed = x km/h 600/x - 600/(x+20) = 2 Solving: x = 60 km/h (by checking options)
Shortcut: Use options: 600/60 - 600/80 = 10 - 7.5 = 2.5 ✓
Concept: Shortcut Techniques - Speed-time relationship
Q7. A 300m train passes a 200m platform in 25 seconds. Find speed. A) 72 km/h B) 79.2 km/h C) 81 km/h D) 86.4 km/h
Answer: A) 72 km/h
Solution: Total distance = 300 + 200 = 500m Speed = 500/25 = 20 m/s = 20 × (18/5) = 72 km/h
Shortcut: Distance = train length + platform length
Concept: Shortcut Techniques - Train crossing platform
Q8. Two trains start from stations 360 km apart at 8 AM and 9 AM with speeds 60 km/h and 90 km/h towards each other. When do they meet? A) 11 AM B) 11:12 AM C) 11:24 AM D) 11:36 AM
Answer: C) 11:24 AM
Solution: In 1st hour (8-9 AM): 1st train covers 60 km Remaining distance = 300 km Relative speed = 60 + 90 = 150 km/h Time = 300/150 = 2 hours Meeting time = 9 AM + 2 hours = 11 AM But 1st train’s head start: 60/150 = 0.4 hours = 24 minutes Actual meeting: 11:24 AM
Shortcut: Account for head start time
Concept: Shortcut Techniques - Meeting point problems
Q9. A train's average speed for onward (60 km/h) and return (40 km/h) journey is: A) 48 km/h B) 50 km/h C) 52 km/h D) 54 km/h
Answer: A) 48 km/h
Solution: Average speed = 2xy/(x+y) = 2×60×40/(60+40) = 4800/100 = 48 km/h
Shortcut: Use harmonic mean formula for equal distances
Concept: Shortcut Techniques - Average speed formula
Q10. A 150m train at 54 km/h crosses another 200m train in 18 seconds. Find second train's speed. A) 36 km/h B) 45 km/h C) 54 km/h D) 72 km/h
Answer: A) 36 km/h
Solution: Total distance = 150 + 200 = 350m Relative speed = 350/18 = 19.44 m/s = 19.44 × (18/5) = 70 km/h First train speed = 54 km/h Second train speed = 70 - 54 = 36 km/h
Shortcut: Convert all to consistent units first
Concept: Shortcut Techniques - Complex relative motion
5 Previous Year Questions
PYQ 1. A train running at 72 km/h crosses a 250m platform in 30 seconds. What is the length of the train? RRB NTPC 2021 CBT-1
Answer: 350m
Solution: Speed = 72 km/h = 72 × (5/18) = 20 m/s Let train length = x meters Total distance = x + 250 Time = 30 seconds x + 250 = 20 × 30 = 600 x = 600 - 250 = 350m
Exam Tip: Always convert km/h to m/s first using 5/18 factor
PYQ 2. Two trains of equal length take 20 seconds and 30 seconds respectively to cross a pole. If they cross each other in 24 seconds when running in opposite directions, find the ratio of their speeds. RRB Group D 2022
Answer: 3:2
Solution: Let length of each train = L meters Speeds: v₁ = L/20, v₂ = L/30 When crossing: 2L/(v₁+v₂) = 24 2L/(L/20 + L/30) = 24 2/(1/20 + 1/30) = 24 2/(3/60) = 24 40 = 24 ✓ Ratio: v₁:v₂ = L/20 : L/30 = 3:2
Exam Tip: Use L as variable and cancel out in ratio problems
PYQ 3. A train covers 480 km. If speed increases by 8 km/h, journey time reduces by 2 hours. Find original speed. RRB ALP 2018
Answer: 40 km/h
Solution: Let original speed = x km/h 480/x - 480/(x+8) = 2 By checking options: 480/40 - 480/48 = 12 - 10 = 2 ✓
Exam Tip: Back-calculate using options when equation is complex
PYQ 4. A 200m train passes a 300m bridge in 25 seconds. Another 150m train passes same bridge in 20 seconds. Find the speed difference. RRB JE 2019
Answer: 9 km/h
Solution: Train 1: (200+300)/25 = 20 m/s = 72 km/h Train 2: (150+300)/20 = 22.5 m/s = 81 km/h Difference = 81 - 72 = 9 km/h
Exam Tip: Remember total distance = train + bridge length
PYQ 5. Two stations 450 km apart. Train A leaves at 60 km/h, Train B leaves 2 hours later at 75 km/h in opposite direction. When do they meet? RPF SI 2019
Answer: 4:40 PM (if A leaves at 10 AM)
Solution: In 2 hours, A covers 120 km Remaining distance = 330 km Relative speed = 60 + 75 = 135 km/h Time = 330/135 = 2.44 hours = 2 hours 26 minutes Meeting time = 12 PM + 2:26 = 2:26 PM
Exam Tip: Account for head start time and distance
Speed Tricks & Shortcuts
| Situation | Shortcut | Example |
|---|---|---|
| km/h to m/s | Multiply by 5/18 | 72 km/h = 72 × 5/18 = 20 m/s |
| m/s to km/h | Multiply by 18/5 | 25 m/s = 25 × 18/5 = 90 km/h |
| Successive Discount | Use (100-net)% | 20% then 20% = 100 - 36 = 64% of original |
| Average Speed (equal distance) | Use 2xy/(x+y) | 40 km/h and 60 km/h = 2×40×60/100 = 48 km/h |
| Percentage of x% | Convert to decimal first | 12.5% of 320 = 0.125 × 320 = 40 |
Common Mistakes to Avoid
| Mistake | Why Students Make It | Correct Approach |
|---|---|---|
| Not converting units | Rushing through problems | Always convert to consistent units first |
| Forgetting train length | Confusing with regular speed problems | Remember: Distance = train + object length |
| Adding/subtracting speeds wrong | Not understanding relative motion | Opposite: add, Same: subtract |
| Using wrong average speed formula | Applying arithmetic mean | Use harmonic mean for equal distances |
| Ignoring digital root check | Not verifying answers | Always check digital root for calculation errors |
Quick Revision Flashcards
| Front (Question/Term) | Back (Answer) |
|---|---|
| km/h to m/s conversion factor | 5/18 |
| m/s to km/h conversion factor | 18/5 |
| Successive 20% change result | 96% of original |
| Average speed formula (equal distance) | 2xy/(x+y) |
| Relative speed (opposite direction) | Add speeds |
| Relative speed (same direction) | Subtract speeds |
| Digital root of 247 | 4 (2+4+7=13, 1+3=4) |
| Unit digit of 17³ | 3 (7×7×7=343) |
| 12.5% as fraction | 1/8 |
| 37.5% as fraction | 3/8 |
Topic Connections
How Shortcut Techniques connects to other RRB exam topics:
- Direct Link: Speed-Distance-Time problems use unit conversion shortcuts extensively
- Combined Questions: Train problems combine relative speed with time-work calculations
- Foundation For: Advanced topics like partnership, mixtures, and compound interest use percentage shortcuts
BETA
