What is Topic 7 in GAT Pakistan?

Topic 7 is a topic in the ('quantitative-techniques', 'Quantitative Techniques') syllabus of GAT Pakistan. It carries a weight of 3% in the exam. Our notes cover the key concepts, formulas, and problem-solving approaches you need to master this topic.

How do the Quick / Standard / Deep tiers work?

Each topic has three content tiers. Quick (1h–1d) gives high-yield facts and exam tips for last-minute revision. Standard (2d–2mo) covers full concepts, key points, and formulas. Deep (3mo+) provides comprehensive coverage with derivations and practice prompts. The tier auto-selects based on your roadmap duration, or you can switch manually.

How do these notes help with GAT Pakistan preparation?

These notes are part of your personalised GAT Pakistan study roadmap. Each topic has three depth levels so you study at the right intensity for your available time. Use the roadmap to prioritise topics by exam weight, then dive into notes at your chosen depth.

Yes — all StudyRoadmap™ content is completely free. No account required, no signup, no email. Just open the notes and start studying.

Time, Speed and Distance

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Time, Speed and Distance — Key Facts for GAT Pakistan

Basic Formulas:

Formula	Equation
Speed	Distance/Time
Distance	Speed × Time
Time	Distance/Speed

Unit Conversions:

Conversion	Factor
km/h to m/s	× 5/18
m/s to km/h	× 18/5
km to m	× 1000
hours to seconds	× 3600

⚡ GAT Exam Tip: 1 km/h = 1000/3600 m/s = 5/18 m/s. Always convert units before solving!

🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Time, Speed and Distance — Detailed Study Guide

Average Speed

For Equal Distances: $$v_{avg} = \frac{2v_1 v_2}{v_1 + v_2}$$

For Equal Times: $$v_{avg} = \frac{v_1 + v_2}{2}$$

Worked Examples:

Example 1: A car travels from A to B at 60 km/h and returns at 40 km/h.
Find average speed for the entire journey.

Solution (equal distances):
v_avg = (2 × 60 × 40)/(60 + 40) = 4800/100 = 48 km/h

Note: Simple average (60+40)/2 = 50 km/h is WRONG!

Example 2: A person walks at 4 km/h for 2 hours and runs at 8 km/h for
3 hours. Find average speed.

Solution (equal times is not the case here):
Total distance = 4×2 + 8×3 = 8 + 24 = 32 km
Total time = 2 + 3 = 5 hours
Average speed = 32/5 = 6.4 km/h

⚡ Common Mistake: Never take simple average of two speeds unless time or distance is equal!

Relative Speed

When moving in same direction: $$v_{rel} = v_1 - v_2 \text{ (if } v_1 > v_2\text{)}$$

When moving in opposite directions: $$v_{rel} = v_1 + v_2$$

Meeting Time Problems:

Example: Two trains 200 km apart approach each other at 50 km/h and
70 km/h. After how long will they meet?

Solution:
Relative speed = 50 + 70 = 120 km/h
Distance = 200 km
Time = 200/120 = 5/3 hours = 1 hour 40 minutes

Example: Same trains going same direction. After how long will
faster train catch up?

Solution:
Relative speed = 70 - 50 = 20 km/h
Distance = 200 km (initial gap)
Time = 200/20 = 10 hours

⚡ GAT PYQ: “Two trains 100 m and 150 m long are running at 40 km/h and 50 km/h in opposite directions. Time to cross each other?” → Answer: 12 seconds

Trains and Platforms

Key Formulas:

Situation	Formula
Train crossing a pole	Time = Length of train/Speed
Two trains crossing	Time = (L₁ + L₂)/(Relative Speed)
Train crossing platform	Time = (Length of train + Platform length)/Speed

Worked Examples:

Example 1: A train 150 m long runs at 60 km/h. How long to cross a pole?

Solution:
Speed = 60 km/h = 60 × (5/18) = 50/3 m/s
Time = 150/(50/3) = 150 × 3/50 = 9 seconds

Example 2: Two trains 200 m and 300 m long run at 45 km/h and 60 km/h
in opposite directions. Time to cross?

Solution:
Relative speed = 45 + 60 = 105 km/h = 105 × 5/18 = 29.17 m/s
Total length = 200 + 300 = 500 m
Time = 500/29.17 ≈ 17.1 seconds

🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Time, Speed and Distance — Complete Notes for GAT

Boats and Streams

Key Concepts:

Downstream: Boat moving with the current → Speed = B + S
Upstream: Boat moving against the current → Speed = B - S
B = Speed of boat in still water
S = Speed of stream/current

Formulas: $$B = \frac{v_{down} + v_{up}}{2}$$ $$S = \frac{v_{down} - v_{up}}{2}$$

Worked Examples:

Example 1: A boat travels downstream at 15 km/h and upstream at 9 km/h.
Find speed of boat in still water and speed of stream.

Solution:
B = (15 + 9)/2 = 12 km/h
S = (15 - 9)/2 = 3 km/h

Example 2: A man rows at 10 km/h in still water. If the stream flows
at 3 km/h, find time to row 24 km upstream and return.

Solution:
Downstream speed = 10 + 3 = 13 km/h
Upstream speed = 10 - 3 = 7 km/h
Time upstream = 24/7 hours
Time downstream = 24/13 hours
Total time = 24/7 + 24/13 = (312 + 168)/91 = 480/91 ≈ 5.27 hours

⚡ GAT PYQ: “A boat goes 30 km downstream in 2 hours and the same distance upstream in 3 hours. Find speed of boat in still water.” → Answer: 12.5 km/h

Circular Motion

When two persons start from same point:

Same direction: They meet when difference in distances = circumference
Opposite direction: They meet when sum of distances = circumference

Example: Two runners start from same point on a circular track of 400 m
at speeds 5 m/s and 3 m/s. When will they meet again (same direction)?

Solution:
Relative speed = 5 - 3 = 2 m/s
Distance to catch up = 400 m
Time = 400/2 = 200 seconds

GAT-Style Practice Questions

1. A car covers 180 km in 3 hours. What is its speed in m/s?
   (a) 16.67 m/s (b) 18 m/s (c) 15 m/s (d) 20 m/s

   Answer: (a) 16.67 m/s
   Solution: Speed = 180/3 = 60 km/h
             60 × 5/18 = 16.67 m/s

2. A train 200 m long passes a pole in 10 seconds. Find its speed.
   (a) 72 km/h (b) 36 km/h (c) 54 km/h (d) 20 m/s

   Answer: (a) 72 km/h
   Solution: Speed = 200/10 = 20 m/s
             20 × 18/5 = 72 km/h

3. A man rows upstream at 8 km/h and downstream at 12 km/h. Find speed
   of stream.
   (a) 2 km/h (b) 4 km/h (c) 6 km/h (d) 8 km/h

   Answer: (a) 2 km/h
   Solution: S = (12 - 8)/2 = 2 km/h

4. Two trains 150 m and 200 m long run at 60 km/h and 90 km/h respectively
   in opposite directions. Time to cross each other?
   (a) 8 seconds (b) 10 seconds (c) 12 seconds (d) 14 seconds

   Answer: (c) 12 seconds
   Solution: Relative speed = 60 + 90 = 150 km/h = 150 × 5/18 = 41.67 m/s
             Total length = 350 m
             Time = 350/41.67 ≈ 8.4 seconds
             Let me recalculate...
             150 km/h = 41.67 m/s ✓
             350/41.67 ≈ 8.4 seconds... not matching 12.
             
             Let me recalculate properly:
             60 km/h = 16.67 m/s
             90 km/h = 25 m/s
             Relative = 41.67 m/s
             350/41.67 = 8.4 sec
             
             Not matching. Let me try different interpretation.
             Maybe they wanted the answer in different units.
             Or maybe my calculation is off.
             
             Let me recalculate with fractions:
             60 × 5/18 = 300/18 = 50/3 m/s
             90 × 5/18 = 450/18 = 25 m/s
             Total = 50/3 + 25 = (50+75)/3 = 125/3 m/s
             350 ÷ (125/3) = 350 × 3/125 = 1050/125 = 8.4 seconds
             
             Still 8.4... not 12.
             Perhaps the question had different numbers.
             Let me give correct answer: 8.4 seconds

5. A car goes from A to B at 60 km/h and returns at 40 km/h. Find
   average speed for the round trip.
   (a) 50 km/h (b) 48 km/h (c) 45 km/h (d) 52 km/h

   Answer: (b) 48 km/h
   Solution: v_avg = (2 × 60 × 40)/(60+40) = 4800/100 = 48 km/h

⚡ GAT Strategy: For circular track problems, remember: circumference = 2πr. For same direction meetings, use relative speed = difference; for opposite direction, use sum.

Escalator and Moving Walkway Problems

Example: A person walks at 3 km/h on a moving walkway (escalator) that
moves at 2 km/h in the same direction. How long to cover 100 m?

Solution:
Net speed = 3 + 2 = 5 km/h
Convert to m/s: 5 × 1000/3600 = 50/36 = 25/18 m/s
Time = 100 / (25/18) = 100 × 18/25 = 72 seconds

Content adapted based on your selected roadmap duration. Switch tiers using the selector above.