SSC CGL Preparation – Day 16

Quantitative Aptitude: Time, Speed, and Distance (TSD)

🔹 1. Key Concepts

🟢 Basic Formulas

• Speed = Distance / Time
• Time = Distance / Speed
• Distance = Speed × Time

🟡 Units Conversion

Unit
1 km = 1000 meters
1 hour = 60 minutes = 3600 seconds
1 m/s = 18/5 km/h
1 km/h = 5/18 m/s

To convert:

• m/s → km/h: multiply by 18/5
• km/h → m/s: multiply by 5/18

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🔹 2. Average Speed

If the same distance is covered at two different speeds: $$\text{Average Speed} = \frac{2xy}{x + y}$$​

where x and y are the speeds for equal distances.

If distances are different: $$\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$$

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🔹 3. Relative Speed

Used when two objects move towards or away from each other.

🔸 Same direction:

$$\text{Relative Speed} = \text{Difference of speeds}$$

🔸 Opposite direction:

$$\text{Relative Speed} = \text{Sum of speeds}$$

Remember to keep units consistent!

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🔹 4. Meeting Point Problems

When two objects start at the same time from different points and move towards each other: $$\text{Time to meet} = \frac{\text{Distance between them}}{\text{Relative speed}}$$

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🔹 5. Train Problems

• Length of train = speed × time

🛤️ If a train crosses a stationary object (pole/tree/person):

$$\text{Time} = \frac{\text{Length of train}}{\text{Speed of train}}$$

🛤️ If a train crosses a platform (or bridge):

$$\text{Time} = \frac{\text{Length of train + Length of platform}}{\text{Speed}}$$

🛤️ Two trains crossing each other:

• Opposite directions: Relative speed = sum of speeds
• Same direction: Relative speed = difference of speeds
  Time = (Sum of lengths) / Relative speed

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🔹 6. Boats and Streams

Let:

• b = speed of boat in still water
• s = speed of stream

Then,

• Downstream speed = b + s
• Upstream speed = b − s

➤ Formulas:

• Time = Distance / Speed (use upstream/downstream accordingly)

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🔹 7. Races

• Lead: Difference in distance covered when one reaches the finish
• If A beats B by d meters in a race of x meters, and B finishes in time t: $$\text{Ratio of speeds} = \frac{x}{x – d}$$

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🔹 8. Important Shortcuts

Situation	Shortcut
Two speeds x and y, same distance	Average speed = (2xy)/(x+y)
Time taken to meet = d / (x ± y)	Depends on direction
Train crosses man/pole	Time = Train length / Speed
Train crosses platform	Time = (Train + Platform length) / Speed
Boat downstream time = D/(b + s)	Upstream = D/(b − s)

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🧠 Tips for SSC CGL

• Time-speed-distance problems are often logic + calculation.
• Always check units (m/s vs km/h).
• In race/boat problems, identify which speed is being referred to.
• Practice train problems with varying objects: poles, platforms, persons.

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✅ Example Problems

🔸 Q1: A train 120 m long runs at 54 km/h. How much time will it take to pass a man standing on a platform?

Solution:
Speed = 54 km/h = (54 × 5)/18 = 15 m/s
Time = 120 / 15 = 8 seconds

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🔸 Q2: A man can row 30 km downstream in 3 hours and the same distance upstream in 6 hours. What is the speed of the boat in still water?

Solution:
Downstream speed = 30/3 = 10 km/h
Upstream speed = 30/6 = 5 km/h
Speed in still water = (10 + 5)/2 = 7.5 km/h

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🔸 Q3: Two trains of lengths 150 m and 200 m are running in opposite directions at 60 km/h and 90 km/h. In how much time will they cross each other?

Solution:
Relative speed = 60 + 90 = 150 km/h = (150 × 5)/18 = 125/3 m/s
Total length = 150 + 200 = 350 m
Time = 350 ÷ (125/3) = (350 × 3)/125 = 8.4 seconds