Time, Speed and Distance – General Aptitude for GATE, PSU, ESE, AE/JE | Priyanka Ma’am

Time, Speed and Distance (TSD) is one of the most important topics in General Aptitude and is frequently asked in GATE, PSU, ESE, AE/JE exams. This topic focuses on motion, relative speed, and practical problem-solving.

Basic Concept

Speed = Distance / Time

Where:

• Distance = Total length covered
• Time = Time taken
• Speed = Distance covered per unit time

Important Formulas

• Speed = Distance / Time
• Distance = Speed × Time
• Time = Distance / Speed
• 1 m/s = 3.6 km/h
• 1 km/h = 5/18 m/s

Key Concepts

1. Average Speed

Average Speed is:

Average Speed = Total Distance / Total Time

For equal distances:

Average Speed = (2 × S1 × S2) / (S1 + S2)

2. Relative Speed

• Same Direction: |S1 − S2|
• Opposite Direction: S1 + S2

3. Boats and Streams

• Downstream Speed = Boat + Stream
• Upstream Speed = Boat − Stream

4. Trains

• Time = Length / Speed
• Crossing pole → Distance = Train length
• Crossing platform → Distance = Train + Platform

Solved Examples

Example 1

A train 120 m long crosses a pole in 6 seconds. Find its speed.

Speed = 120 / 6 = 20 m/s
= 20 × 3.6 = 72 km/h

Example 2

A man travels 60 km at 30 km/h and returns at 20 km/h. Find average speed.

Average Speed = (2 × 30 × 20) / (30 + 20)
= 1200 / 50 = 24 km/h

Example 3

Two trains moving in opposite directions at 40 km/h and 60 km/h. Find relative speed.

Relative Speed = 40 + 60 = 100 km/h

Example 4 (GATE Level)

A boat goes 30 km downstream in 2 hours and returns upstream in 3 hours. Find speed of stream.

Downstream = 30/2 = 15 km/h
Upstream = 30/3 = 10 km/h
Stream speed = (15 − 10)/2 = 2.5 km/h

Shortcut Tricks

• If speed increases by x%, time decreases by x/(100 + x)%
• If speed decreases by x%, time increases by x/(100 − x)%
• Use ratio method to solve faster
• Convert units properly before solving

Previous Year Concept Type Questions

Q1. A train 150 m long crosses a pole in 5 seconds. Find speed.

Speed = 150/5 = 30 m/s = 108 km/h

Q2. A person travels equal distances at 40 km/h and 60 km/h. Find average speed.

Average Speed = (2 × 40 × 60) / (40 + 60) = 4800/100 = 48 km/h

Exam Tips

• Always check unit conversion
• Use formulas smartly instead of lengthy calculations
• Practice train and relative speed problems more
• Solve PYQs to understand patterns

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