SSC CGL Preparation – Day 8

Quantitative Aptitude: Time and Distance

📘 Concept Overview

“Time and Distance” is a fundamental topic in quantitative aptitude. It includes questions related to:

• Constant speed
• Relative speed
• Units conversion
• Train-based problems
• Boats & streams
• Circular tracks

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📏 Basic Formulas

1. Distance = Speed × Time

• If any two are known, the third can be calculated.

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2. Speed = Distance / Time

3. Time = Distance / Speed

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4. Unit Conversions

Quantity	Conversion
1 km	1000 meters
1 hour	60 minutes
1 minute	60 seconds
1 km/hr	(5/18) m/s
1 m/s	(18/5) km/hr

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5. Average Speed

If equal distances are covered at two different speeds: $$\text{Average Speed} = \frac{2xy}{x + y}$$

Where x and y are two speeds.

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6. Relative Speed

• Same direction: $$\text{Relative Speed} = \text{Faster speed} – \text{Slower speed}$$
• Opposite direction: $$\text{Relative Speed} = \text{Sum of both speeds}$$

Always convert to same units (m/s or km/hr).

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7. Time to Cross an Object

• If a train of length L meters is moving at speed S m/s:
  • To cross a pole: $$\text{Time} = \frac{L}{S}$$
  • To cross a platform of length P: $$\text{Time} = \frac{L + P}{S}$$

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8. Boats and Streams

• Downstream Speed = Boat speed + Stream speed
• Upstream Speed = Boat speed – Stream speed
• If downstream speed = D and upstream speed = U: $$\text{Boat speed} = \frac{D + U}{2},$$ $$\quad \text{Stream speed} = \frac{D – U}{2}$$

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9. Circular Track

If A and B start at the same time:

• Same direction: $$\frac{\text{Total distance}}{\text{Relative Speed (difference)}}$$
• Opposite direction: $$\frac{\text{Total distance}}{\text{Relative Speed (sum)}}$$

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✏️ Examples

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Example 1:
A person covers 90 km at a speed of 30 km/hr. Find the time taken.

Solution: $$\text{Time} = \frac{90}{30} = 3 \text{ hours}$$

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Example 2:
Convert 72 km/hr to m/s. =$$72 \times \frac{5}{18} = 20 \text{ m/s}$$

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Example 3:
Two trains of lengths 150m and 100m run at 45 km/hr and 35 km/hr in opposite directions. Find the time to cross each other.

Solution:
Convert speed:
Total relative speed = 45 + 35 = 80 km/hr
= 80 × 5/18 = 400/18 = 22.22 m/s

Total length = 150 + 100 = 250 m

Time = 250 / 22.22 ≈ 11.25 seconds

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Example 4:
A boat takes 2 hours to go downstream and 3 hours to return upstream for the same distance. Find the ratio of speed of boat to stream.

Solution:
Let distance = D
Downstream speed = D/2
Upstream speed = D/3
Ratio = (D/2 + D/3) : (D/2 – D/3)
= (5D/6) : (D/6) = 5:1

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💡 Quick Tips & Tricks

1. Convert units first before solving (km/hr to m/s if needed).
2. Train/platform → Add lengths.
3. Time = Distance / Speed — ensure same units.
4. For equal distance, Average speed ≠ arithmetic mean — use formula.
5. For trains passing each other or platforms, total distance = sum of lengths.
6. For relative motion, always consider direction carefully.