SSC CGL 2027 Time-Speed-Distance Questions Using Relative Speed

Time, Speed and Distance is an important topic in the Quantitative Aptitude section of SSC CGL 2027. Questions based on relative speed are commonly solved using a few simple formulas and logical calculations. Understanding the difference between objects moving in the same direction and opposite directions can help candidates solve these questions more quickly and accurately.

In this article, you will learn the important formulas, solved examples, shortcut methods and practice questions on relative speed for SSC CGL Tier 1 and Tier 2 preparation.

1. What Is Relative Speed?

Relative speed is the speed of one object with respect to another moving object. It helps us calculate how quickly the distance between two moving objects changes.

Relative speed is mainly used in questions involving two trains, two people running, vehicles travelling on a road, and objects moving towards or away from each other.

2. Important Relative Speed Formulas

When two objects move in the same direction:

Relative Speed = Speed of Faster Object − Speed of Slower Object

When two objects move in opposite directions:

Relative Speed = Speed of First Object + Speed of Second Object

Time taken to meet or overtake:

Time = Distance between Objects ÷ Relative Speed

Unit conversion:

• km/h to m/s: Multiply by 5/18.
• m/s to km/h: Multiply by 18/5.

Important: Make sure speed and distance use compatible units before applying a formula. If distance is given in metres, convert speed into metres per second when calculating time in seconds.

3. Relative Speed in the Same Direction

When two objects move in the same direction, their relative speed is the difference between their speeds. The faster object catches up with the slower object at this speed.

Example 1: Two cars travel in the same direction at 72 km/h and 54 km/h. If the faster car is 90 metres behind the slower car, how much time will it take to catch up?

Solution:

• Relative speed = 72 − 54 = 18 km/h
• Convert into m/s = 18 × 5/18 = 5 m/s
• Time = 90 ÷ 5 = 18 seconds

Answer: 18 seconds

4. Relative Speed in Opposite Directions

When two objects move towards each other, their relative speed is the sum of their individual speeds. The distance between them decreases at this combined rate.

Example 2: Two cyclists are 300 metres apart and move towards each other at 6 m/s and 4 m/s. Find the time taken for them to meet.

Solution:

• Relative speed = 6 + 4 = 10 m/s
• Time = 300 ÷ 10 = 30 seconds

Answer: 30 seconds

5. Relative Speed Questions Involving Trains

Relative speed is especially useful in train problems. When two trains cross each other, the total distance covered is generally the sum of their lengths. When one train crosses a stationary pole, the distance covered is the length of that train.

Example 3: Two trains of lengths 120 metres and 180 metres travel in opposite directions at 54 km/h and 36 km/h. Calculate the time taken to cross each other completely.

Solution:

• Total distance = 120 + 180 = 300 metres
• Relative speed = 54 + 36 = 90 km/h
• Convert speed = 90 × 5/18 = 25 m/s
• Time = 300 ÷ 25 = 12 seconds

Answer: 12 seconds

6. Relative Speed When One Object Overtakes Another

Overtaking questions usually involve objects moving in the same direction. The relative speed is the difference between their speeds, while the distance covered to complete the overtake depends on the question.

Example 4: A train 150 metres long travels at 72 km/h and overtakes a train 100 metres long moving in the same direction at 54 km/h. Find the time required to cross the slower train completely.

Solution:

• Total distance = 150 + 100 = 250 metres
• Relative speed = 72 − 54 = 18 km/h
• Relative speed in m/s = 18 × 5/18 = 5 m/s
• Time = 250 ÷ 5 = 50 seconds

Answer: 50 seconds

7. Quick Tricks to Solve Relative Speed Questions

• Same direction: Subtract the speeds.
• Opposite directions: Add the speeds.
• Meeting time: Divide the distance between objects by relative speed.
• Train crossing train: Add both train lengths to obtain the total distance.
• Train crossing a pole: Use only the train's length as the distance.
• Convert units first: Use m/s when the distance is in metres and the required time is in seconds.
• Check the question: Identify whether the objects are approaching, separating or overtaking before selecting a formula.

8. Practice Questions for SSC CGL 2027

Attempt the following multiple-choice questions to test your understanding of relative speed.

Question 1: Two cars travel in the same direction at 80 km/h and 60 km/h. What is their relative speed?

• A) 10 km/h
• B) 20 km/h
• C) 40 km/h
• D) 140 km/h

Question 2: Two runners move towards each other at 5 m/s and 7 m/s. They are initially 144 metres apart. How long will they take to meet?

• A) 10 seconds
• B) 12 seconds
• C) 14 seconds
• D) 18 seconds

Question 3: A train travelling at 72 km/h overtakes a person walking in the same direction at 6 km/h. If the train is 220 metres long, how much time does it take to pass the person completely?

• A) 10 seconds
• B) 11 seconds
• C) 12 seconds
• D) 15 seconds

Question 4: Two trains, each 150 metres long, travel in opposite directions at 45 km/h and 63 km/h. Find the time taken to cross each other.

• A) 8 seconds
• B) 10 seconds
• C) 12 seconds
• D) 15 seconds

Question 5: Two bikes are moving in the same direction at 15 m/s and 10 m/s. If the faster bike is 100 metres behind the slower bike, how long will it take to catch up?

• A) 10 seconds
• B) 15 seconds
• C) 20 seconds
• D) 25 seconds

9. Answers with Explanations

1. B) 20 km/h
Same direction: 80 − 60 = 20 km/h.

2. B) 12 seconds
Relative speed = 5 + 7 = 12 m/s. Time = 144 ÷ 12 = 12 seconds.

3. B) 11 seconds
Relative speed = 72 − 6 = 66 km/h. In m/s, 66 × 5/18 = 55/3 m/s. Time = 220 ÷ (55/3) = 12 seconds. Therefore, the correct answer is C) 12 seconds.

4. B) 10 seconds
Total length = 150 + 150 = 300 metres. Relative speed = 45 + 63 = 108 km/h = 30 m/s. Time = 300 ÷ 30 = 10 seconds.

5. C) 20 seconds
Relative speed = 15 − 10 = 5 m/s. Time = 100 ÷ 5 = 20 seconds.

10. How to Prepare Relative Speed for SSC CGL 2027

Begin by memorising the formulas for same-direction and opposite-direction movement. Practise unit conversion regularly and solve questions involving meeting time, overtaking and train crossing. Start with basic problems before moving to multi-step questions.

During mock tests, read each question carefully and identify the direction of movement before calculating relative speed. Review incorrect answers to understand whether the mistake occurred in the formula, unit conversion or calculation.

Conclusion

Relative speed is a useful concept for solving Time, Speed and Distance questions in SSC CGL 2027. By understanding when to add or subtract speeds, converting units correctly and practising train and overtaking problems, candidates can improve their speed and accuracy in Quantitative Aptitude.

Revise the formulas regularly and practise a variety of questions to strengthen your SSC CGL Maths preparation.