Time Speed Distance - Quantitative Aptitude for SSC CGL

1. Introduction

This topic is a core part of SSC CGL Quantitative Aptitude — and one of the most formula-based and score-friendly chapters. You'll often find direct questions on relative speed, train problems, and boats & streams — all using the same base formula:

Speed = Distance / Time

or

Distance = Speed × Time

2. Unit Conversion

1 km/hr = 5/18 m/s

1 m/s = 18/5 km/hr

Always convert all speeds to the same unit before solving.

Example 1

Convert 90 km/hr into m/s

90 × 5/18 = 25 m/s

25 m/s

3. Core Formula Set

Concept	Formula	Notes
Speed	Distance / Time	-
Distance	Speed × Time	-
Time	Distance / Speed	-
km/hr → m/s	× 5/18	-
m/s → km/hr	× 18/5	-

4. Relative Speed

When two bodies move towards or away from each other:

Case	Relative Speed
Same Direction	v₁ - v₂
Opposite Direction	v₁ + v₂

Example 2

Two trains of speeds 60 km/hr and 40 km/hr run in opposite directions. Find their relative speed.

= 60 + 40 = 100 km/hr

Relative speed = 100 km/hr

Example 3

Two cars run in the same direction at 80 km/hr and 50 km/hr. Find their relative speed.

= 80 - 50 = 30 km/hr

Relative speed = 30 km/hr

5. Train Problems

Time = Length of Train (or sum of trains) / Relative Speed

Convert speed into m/s when length is in meters.

Example 4

A train 180 m long passes a pole in 6 seconds. Find its speed.

Speed = 180/6 = 30 m/s = 30 × 18/5 = 108 km/hr

Speed = 108 km/hr

Example 5

A train 120 m long crosses another train 180 m long in 9 seconds while moving in opposite directions at speeds 60 km/hr and 40 km/hr. Find the time.

Relative speed = 60 + 40 = 100 km/hr = 100 × 5/18 = 27.78 m/s

Distance = 120 + 180 = 300 m

Time = 300/27.78 ≈ 10.8 sec

Time ≈ 10.8 sec

6. Boats and Streams

Type	Formula
Speed in still water	(Downstream + Upstream) / 2
Speed of stream	(Downstream - Upstream) / 2

Example 6

A boat goes 12 km downstream in 3 hours and returns in 4 hours. Find speed of boat in still water and of stream.

Downstream speed = 12/3 = 4, Upstream = 12/4 = 3

Boat speed = (4 + 3)/2 = 3.5 km/hr

Stream speed = (4 - 3)/2 = 0.5 km/hr

Boat = 3.5 km/hr, Stream = 0.5 km/hr

Example 7

If a boat's speed in still water is 8 km/hr and stream's speed is 2 km/hr, find downstream and upstream speed.

Downstream = 8 + 2 = 10 km/hr

Upstream = 8 - 2 = 6 km/hr

10 km/hr, 6 km/hr

7. Shortcut Methods for SSC

Case	Shortcut
Distance constant	S₁T₁ = S₂T₂ ⇒ T₁/T₂ = S₂/S₁
Average speed (equal distance)	2S₁S₂ / (S₁ + S₂)
Train crosses platform	(L_train + L_platform) / Speed
Boats & streams	Still water = (D + U)/2, Stream = (D - U)/2
Meeting point (same direction)	Time = Distance between them / (V₁ - V₂)

Example 8 (Average Speed Shortcut)

A car goes 60 km at 30 km/hr and returns at 60 km/hr. Find average speed.

Avg speed = (2×30×60)/(30+60) = 3600/90 = 40 km/hr

Average Speed = 40 km/hr

8. Practice Section

Q1. A train 150 m long passes a pole in 10 seconds. Find its speed in km/hr.

View Answer

Speed = 150/10 = 15 m/s = 15×18/5 = 54 km/hr

54 km/hr

Q2. A train 200 m long passes a man walking at 6 km/hr in the same direction in 9 seconds. Find the speed of the train.

View Answer

Relative speed = 200/9 = 22.22 m/s = 22.22×18/5 = 80 km/hr

Train speed = 80 + 6 = 86 km/hr

86 km/hr

Q3. Two trains of lengths 120 m and 180 m cross each other in 12 seconds while running opposite. Speeds are 50 km/hr and 40 km/hr. Verify.

View Answer

Relative speed = 90×5/18 = 25 m/s

Time = 300/25 = 12 sec

12 sec

Q4. A boat goes 24 km downstream in 3 hours and 18 km upstream in 6 hours. Find the boat and stream speed.

View Answer

Down = 8 km/hr, Up = 3 km/hr

Boat = (8+3)/2 = 5.5, Stream = (8–3)/2 = 2.5

5.5 km/hr, 2.5 km/hr

Q5. Two cars start from the same point. One at 60 km/hr, another at 90 km/hr. How long before they are 60 km apart?

View Answer

Rel. speed = 90–60 = 30 km/hr

Time = 60/30 = 2 hr

2 hours

Q6. A train crosses a 300 m platform in 20 s and a signal post in 12 s. Find its length and speed.

View Answer

Speed = (L/12) = (L+300)/20 ⇒ 20L = 12L + 3600 ⇒ L = 450 m

Speed = 450/12 = 37.5 m/s = 135 km/hr

450 m, 135 km/hr

Q7. A car travels 240 km at uniform speed. If it increases speed by 20 km/hr, it takes 1 hour less. Find its original speed.

View Answer

240/x - 240/(x+20) = 1 ⇒ x(x+20) = 4800 ⇒ x² + 20x - 4800 = 0 ⇒ x=60

Speed = 60 km/hr

9. Quick Summary Table

Concept	Formula	Key Idea
Speed	D/T	Core relation
Relative Speed	v₁ ± v₂	Opposite (+), Same (−)
Train crosses pole	T = L/S	Length matters
Average Speed	2S₁S₂/(S₁ + S₂)	Equal distance
Boats (Still water)	(D + U)/2	Add divide 2
Stream	(D - U)/2	Subtract divide 2

You've completed Article 7: Time, Speed & Distance!

Courage Tip: Before solving, check if the question involves trains, streams, or two moving bodies — each has a fixed logic but the same formula base: "Speed × Time = Distance."

Time, Speed & Distance

1. Introduction

2. Unit Conversion

Example 1

3. Core Formula Set

4. Relative Speed

Example 2

Example 3

5. Train Problems

Example 4

Example 5

6. Boats and Streams

Example 6

Example 7

7. Shortcut Methods for SSC

Example 8 (Average Speed Shortcut)

8. Practice Section

Q1. A train 150 m long passes a pole in 10 seconds. Find its speed in km/hr.

Q2. A train 200 m long passes a man walking at 6 km/hr in the same direction in 9 seconds. Find the speed of the train.

Q3. Two trains of lengths 120 m and 180 m cross each other in 12 seconds while running opposite. Speeds are 50 km/hr and 40 km/hr. Verify.

Q4. A boat goes 24 km downstream in 3 hours and 18 km upstream in 6 hours. Find the boat and stream speed.

Q5. Two cars start from the same point. One at 60 km/hr, another at 90 km/hr. How long before they are 60 km apart?

Q6. A train crosses a 300 m platform in 20 s and a signal post in 12 s. Find its length and speed.

Q7. A car travels 240 km at uniform speed. If it increases speed by 20 km/hr, it takes 1 hour less. Find its original speed.

9. Quick Summary Table

You've completed Article 7: Time, Speed & Distance!

Start Your SSC CGL Journey Now!