Question 1

Two trains start simultaneously from stations A and B, which are 450 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards A at 90 km/h. After how much time will they meet, and at what distance from station A?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = sum of individual speeds. Relative speed = 60 + 90 = 150 km/h. Step 2: Time to meet = Total distance / Relative speed = 450 / 150 = 3 hours. Step 3: Distance of meeting point from A = Speed of Train X × Time = 60 × 3 = 180 km. Step 4: Verify: Distance from B = 90 × 3 = 270 km. Total = 180 + 270 = 450 km ✓. Therefore, trains meet after 3 hours at a distance of 180 km from station A.

Question 2

A cyclist and a runner start from the same point and move in the same direction. The cyclist travels at 24 km/h and the runner at 8 km/h. After how much time will the cyclist be 32 km ahead of the runner?

Accepted Answer

Step 1: When two objects move in the same direction, their relative speed is the difference of their speeds. Relative speed = 24 - 8 = 16 km/h. Step 2: Time = Distance ÷ Relative Speed = 32 ÷ 16 = 2 hours. Therefore, the answer is 2 hours.

Question 3

A boat travels downstream at 15 km/h and upstream at 9 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. Downstream: B + C = 15. Upstream: B - C = 9. Step 2: Add both equations: (B + C) + (B - C) = 15 + 9 → 2B = 24 → B = 12 km/h. Therefore, the speed of the boat in still water is 12 km/h.

Question 4

Two cars start from the same location and travel in opposite directions. Car X travels at 50 km/h and Car Y travels at 70 km/h. How far apart will they be after 3 hours?

Accepted Answer

Step 1: When two objects travel in opposite directions, their relative speed is the sum of their individual speeds. Relative speed = 50 + 70 = 120 km/h. Step 2: Distance = Relative Speed × Time = 120 × 3 = 360 km. Therefore, the cars will be 360 km apart after 3 hours.

Question 5

A person walks at 4 km/h. If he walks for 2.5 hours, how many metres does he cover?

Accepted Answer

Step 1: Distance = Speed × Time = 4 km/h × 2.5 h = 10 km. Step 2: Convert km to metres: 10 km = 10 × 1000 = 10,000 metres.

Question 6

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 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 7

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 = difference of speeds = 15 - 10 = 5 km/h. Step 2: The man needs to cover the initial gap of 30 km at this relative speed. Step 3: Time = 30 ÷ 5 = 6 hours.

Question 8

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 boat in still water = b km/h and speed of current = c km/h. Step 2: Upstream speed: b - c = 8. Downstream speed: b + c = 12. Step 3: Adding both equations: 2b = 20, so b = 10 km/h.

Question 9

Two runners start from the same point and run in opposite directions. Runner A runs at 12 km/h and Runner B runs at 8 km/h. After how many hours will they be 60 km apart?

Accepted Answer

Step 1: When runners move in opposite directions, their relative speed = sum of speeds = 12 + 8 = 20 km/h. Step 2: Time to be 60 km apart = Distance ÷ Relative speed = 60 ÷ 20 = 3 hours.

Question 10

A car travels 120 km in 2 hours. A motorcycle travels at a speed 25% faster than the car. How far will the motorcycle travel in 3 hours?

Accepted Answer

Step 1: Car's speed = 120 ÷ 2 = 60 km/h. Step 2: Motorcycle's speed = 60 + (25% of 60) = 60 + 15 = 75 km/h. Step 3: Distance covered by motorcycle in 3 hours = 75 × 3 = 225 km.

Question 11

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 200 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 = 200 ÷ 100 = 2 hours. Therefore, the answer is 2 hours.

Question 12

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 20 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 = difference of speeds = 15 − 10 = 5 km/h. Step 2: The man needs to cover the 20 km gap at this relative speed. Time = 20 ÷ 5 = 4 hours.

Question 13

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

Accepted Answer

Step 1: Let the speed of the boat in still water be b km/h and the speed of the current be c km/h. Upstream speed: b − c = 8. Downstream speed: b + c = 12. Step 2: Add both equations: (b − c) + (b + c) = 8 + 12, so 2b = 20, thus b = 10 km/h. Step 3: Subtract the first from the second: (b + c) − (b − c) = 12 − 8, so 2c = 4, thus c = 2 km/h. Therefore, boat speed = 10 km/h and current speed = 2 km/h.

Question 14

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 currently 150 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. Relative speed = 60 + 40 = 100 km/h. Step 2: Time = Distance ÷ Relative Speed = 150 ÷ 100 = 1.5 hours.

Question 15

A train passes a stationary pole in 8 seconds. The same train passes a platform of length 240 m in 20 seconds. What is the speed of the train in km/h?

Accepted Answer

Step 1: Let the length of the train be L metres. When passing a pole, the train covers its own length in 8 seconds: L = Speed × 8. Step 2: When passing the platform, the train covers L + 240 in 20 seconds: L + 240 = Speed × 20. Step 3: From equation 1: Speed = L/8. Substituting in equation 2: L + 240 = (L/8) × 20 = 2.5L. So 240 = 1.5L, giving L = 160 m. Step 4: Speed = 160/8 = 20 m/s = 20 × 3.6 = 72 km/h.

Question 16

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. Relative speed = 60 + 40 = 100 km/h. Step 2: Time = Distance ÷ Relative Speed = 500 ÷ 100 = 5 hours. Therefore, the trains will meet in 5 hours.

Question 17

A man walks at 5 km/h and a boy cycles at 15 km/h in the same direction on a straight road. If the boy is initially 10 km behind the man, how long will it take for the boy to catch up with the man?

Accepted Answer

Step 1: When both move in the same direction, relative speed = faster speed − slower speed = 15 − 5 = 10 km/h. Step 2: The boy needs to cover the initial gap of 10 km at the relative speed. Time = Distance ÷ Relative Speed = 10 ÷ 10 = 1 hour. Therefore, the boy will catch up in 1 hour.

Question 18

Two cyclists start from the same point and travel in opposite directions. Cyclist A travels at 12 km/h and Cyclist B travels at 18 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 individual speeds. Relative speed = 12 + 18 = 30 km/h. Step 2: Time = Distance ÷ Relative Speed = 90 ÷ 30 = 3 hours. Therefore, they will be 90 km apart after 3 hours.

Question 19

A car travels from City A to City B at 60 km/h and returns from City B to City A at 40 km/h. If the distance between the cities is 120 km, what is the average speed for the entire journey?

Accepted Answer

Step 1: Total distance = 120 + 120 = 240 km. Step 2: Time for A to B = 120 ÷ 60 = 2 hours. Time for B to A = 120 ÷ 40 = 3 hours. Total time = 2 + 3 = 5 hours. Step 3: Average speed = Total distance ÷ Total time = 240 ÷ 5 = 48 km/h.

Question 20

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

Accepted Answer

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

Question 21

Two trains start simultaneously from stations A and B, which are 480 km apart. Train X travels from A towards B at 60 km/h, while Train Y travels from B towards 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 before the two trains meet?

Accepted Answer

Step 1: Find the relative speed of the two trains moving towards each other: 60 + 40 = 100 km/h. Step 2: Calculate the time taken for the trains to meet: Time = Distance ÷ Relative Speed = 480 ÷ 100 = 4.8 hours. Step 3: The bird flies continuously at 80 km/h for the entire 4.8 hours until the trains meet. Step 4: Distance covered by bird = Speed × Time = 80 × 4.8 = 384 km.

SSC CHSL Relative Speed

SSC CHSL 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