Question 1

Two cars start from the same location and travel towards each other on a straight road. Car P travels at 55 km/h and Car Q travels at 65 km/h. If they meet after 4 hours, what was the initial distance between them?

Accepted Answer

Step 1: Since the cars travel towards each other, their relative speed is the sum of their individual speeds. Relative speed = 55 + 65 = 120 km/h. Step 2: Distance = Relative Speed × Time = 120 × 4 = 480 km. Therefore, the initial distance between them was 480 km.

Question 2

A runner jogs at 12 km/h and a cyclist rides at 18 km/h, both starting from the same point in the same direction. After 2 hours, how far ahead is the cyclist from the runner?

Accepted Answer

Step 1: The relative speed between the cyclist and runner is 18 - 12 = 6 km/h (since they move in the same direction). Step 2: After 2 hours, the distance covered by the cyclist relative to the runner is: Distance = Relative Speed × Time = 6 × 2 = 12 km. Therefore, the cyclist is 12 km ahead.

Question 3

A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the woman starts 30 km ahead, how long will it take the man to catch up with the woman?

Accepted Answer

Step 1: When both move in the same direction, relative speed = faster speed − slower speed = 15 − 10 = 5 km/h. Step 2: The man needs to cover the initial gap of 30 km at the relative speed. Step 3: Time = Distance ÷ Relative speed = 30 ÷ 5 = 6 hours.

Question 4

Two trains of lengths 150 m and 100 m are running towards each other on parallel tracks at speeds of 50 km/h and 40 km/h respectively. How many seconds will they take to completely pass each other?

Accepted Answer

Step 1: Convert speeds to m/s: 50 km/h = 50 × (5/18) = 13.89 m/s (approx), 40 km/h = 40 × (5/18) = 11.11 m/s (approx). Step 2: For cleaner calculation: relative speed = 50 + 40 = 90 km/h = 90 × (5/18) = 25 m/s. Step 3: Total distance to cover = 150 + 100 = 250 m. Step 4: Time = 250 ÷ 25 = 10 seconds.

Question 5

A train 240 metres long is travelling at 45 km/h. How long will it take to pass a stationary pole?

Accepted Answer

Step 1: Convert train speed to m/s: 45 km/h = 45 × (5/18) = 12.5 m/s. Step 2: To pass a pole, the train must cover a distance equal to its own length (240 m). Step 3: Time = Distance ÷ Speed = 240 ÷ 12.5 = 19.2 seconds.

Question 6

Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 18 km/h and Cyclist B travels at 12 km/h. After how many hours will they be 90 km apart?

Accepted Answer

Step 1: When two objects move in opposite directions, their relative speed is the sum of their speeds. Step 2: Relative speed = 18 + 12 = 30 km/h. Step 3: Time = Distance ÷ Relative speed = 90 ÷ 30 = 3 hours.

Question 7

Two trains are running towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 500 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Time = Distance ÷ Relative speed = 500 ÷ 100 = 5 hours.

Question 8

Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A to B at 60 km/h, while Train Y travels from B to A at 40 km/h. A bird flies back and forth between the two trains at a constant speed of 80 km/h, starting from Train X. What is the total distance covered by the bird from the moment the trains start until they meet?

Accepted Answer

Step 1: Find the time taken for the two trains to meet. Relative speed = 60 + 40 = 100 km/h (opposite directions). Time to meet = 480 ÷ 100 = 4.8 hours. Step 2: The bird flies continuously at 80 km/h for the entire 4.8 hours until the trains meet. Distance covered by bird = 80 × 4.8 = 384 km. Therefore, the answer is 384 km.

Question 9

A train 150 m long travels at 72 km/h. A man stands on a platform. How long does the train take to completely pass the man?

Accepted Answer

Step 1: Convert train speed from km/h to m/s: 72 km/h = 72 × (5/18) = 20 m/s. Step 2: For the train to completely pass the man, the entire length of the train (150 m) must go past the man's point. Step 3: Time = Distance ÷ Speed = 150 ÷ 20 = 7.5 seconds. Therefore, the answer is 7.5 seconds.

Question 10

A boat travels 120 km downstream in 4 hours and 120 km upstream in 6 hours. A second boat travels at twice the speed of the current. How long will the second boat take to travel 180 km downstream?

Accepted Answer

Step 1: Let boat speed = b, current speed = c. Downstream: (b + c) × 4 = 120, so b + c = 30 km/h. Upstream: (b - c) × 6 = 120, so b - c = 20 km/h. Step 2: Solving: 2b = 50, so b = 25 km/h and c = 5 km/h. Step 3: Second boat speed = 2c = 10 km/h. Step 4: Downstream speed of second boat = 10 + 5 = 15 km/h. Step 5: Time = 180 ÷ 15 = 12 hours. Therefore, the answer is 12 hours.

Question 11

Two cars start from the same point on a circular track of circumference 600 m. Car A travels at 15 m/s and Car B travels at 10 m/s, both in the same direction. After how much time will Car A lap Car B for the second time?

Accepted Answer

Step 1: Car A laps Car B when the difference in distances traveled equals the circumference of the track. Relative speed = 15 - 10 = 5 m/s. Step 2: Time for first lap = 600 ÷ 5 = 120 seconds. Step 3: For the second lap, Car A must gain another 600 m on Car B. Time for second lap = 600 ÷ 5 = 120 seconds. Step 4: Total time for second lap = 120 + 120 = 240 seconds. Therefore, the answer is 240 seconds.

Question 12

Two buses start from the same point and travel in opposite directions. Bus X travels at 50 km/h and Bus Y travels at 30 km/h. After how many hours will they be 240 km apart?

Accepted Answer

Step 1: When two objects travel in opposite directions, their relative speed is the sum of their individual speeds. Relative speed = 50 + 30 = 80 km/h. Step 2: Time = Distance ÷ Relative Speed = 240 ÷ 80 = 3 hours. Therefore, the answer is 3 hours.

Question 13

Two trains are moving towards each other on parallel tracks. Train A travels at 60 km/h and Train B travels at 40 km/h. If they are initially 300 km apart, how long will it take for them to meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed is the sum of their individual speeds. Relative speed = 60 + 40 = 100 km/h. Step 2: Time = Distance ÷ Relative Speed = 300 ÷ 100 = 3 hours. Therefore, the answer is 3 hours.

Question 14

A man cycles at 15 km/h and a woman cycles at 10 km/h in the same direction on the same road. If the man starts 50 km behind the woman, how long will it take for the man to catch up with the woman?

Accepted Answer

Step 1: When both move in the same direction, relative speed is the difference of their speeds. Relative speed = 15 - 10 = 5 km/h. Step 2: The man needs to cover the 50 km gap at this relative speed. Time = Distance ÷ Relative Speed = 50 ÷ 5 = 10 hours. Therefore, the answer is 10 hours.

Question 15

A boat travels upstream at 8 km/h and downstream at 12 km/h. What is the speed of the boat in still water?

Accepted Answer

Step 1: Let the speed of the boat in still water be B and the speed of the current be C. Upstream speed: B - C = 8. Downstream speed: B + C = 12. Step 2: Add both equations: (B - C) + (B + C) = 8 + 12, which gives 2B = 20, so B = 10 km/h. Therefore, the speed of the boat in still water is 10 km/h.

SSC CPO Relative Speed

SSC CPO Relative Speed — Past Exam Questions

Relative Speed— Rules & Concept

Key Points to Remember

Exam-Specific Tips

Relative Speed — Practice Questions

60-Second Revision — Relative Speed