Analytical Skills-II
Unit 4: Time-Speed-Distance, Trains & Boats
From basic formulas to Rajdhani vs Garib Rath problems — master every type of speed question asked in competitive exams with shortcuts and visual methods.
⏱ 6 hrs theory + 4 hrs practice | 🎯 Railway/Bank/TCS | 💰 ₹8-12 marks in exams
📝 30 MCQs (Bloom's Mapped) | 8 Short Answers | 3 Long Answers | 40+ Worked Problems
Opening Hook — The Mathematics Behind Every Journey
🚂 How Indian Railways Runs 13,000 Trains Daily Without Collision
Every single day, Indian Railways operates 13,000+ trains carrying 23 million passengers across 68,000+ km of track. How do they ensure a Rajdhani Express (130 km/h) doesn't crash into a Garib Rath (80 km/h) running on the same track? The answer: relative speed calculations.
Railway engineers use time-speed-distance formulas to compute safe headway distances, overtaking points, and crossing times. The Centre for Railway Information Systems (CRIS) runs algorithms that are essentially the same problems you'll solve in this chapter — just at massive scale.
Meanwhile, Uber and Ola calculate your ETA using the same S = D/T formula, adjusted for real-time traffic. And Boats & Streams? They appear in EVERY single bank exam — SBI PO, IBPS, RRB — guaranteed 2-3 questions worth 6-10 marks.
Master this chapter, and you master the most high-ROI topic in quantitative aptitude.
Learning Outcomes — Bloom's Taxonomy Mapped
| Bloom's Level | Learning Outcome |
|---|---|
| 🔵 Remember | Recall the formulas S = D/T, D = S×T, T = D/S and unit conversion factors (×5/18 and ×18/5) |
| 🔵 Remember | State the formulas for relative speed in same and opposite directions |
| 🟢 Understand | Explain why average speed ≠ arithmetic mean of speeds with a counter-example |
| 🟢 Understand | Describe the difference between upstream and downstream speed in boats & streams |
| 🟡 Apply | Solve train passing pole, platform, and bridge problems using standard formulas |
| 🟡 Apply | Calculate meeting point and overtaking time for two objects moving in same/opposite directions |
| 🟠 Analyze | Decompose complex multi-step problems (e.g., trains on a bridge with a man walking) into sub-problems |
| 🟠 Analyze | Compare different approaches (formula vs ratio method) and identify the fastest strategy for exam conditions |
| 🔴 Evaluate | Assess which shortcut method (proportionality, product consistency, ratio) applies to a given word problem |
| 🔴 Evaluate | Judge whether a given answer is reasonable by estimating using approximations |
| 🟣 Create | Design original word problems involving trains and boats for peer practice |
| 🟣 Create | Construct a complete solution with Given → Find → Formula → Solution → Shortcut → Boxed Answer |