Question 1

Two cyclists start from the same point and travel in the same direction on a circular track of 600 m. Cyclist A travels at 15 m/s and Cyclist B at 10 m/s. After how many seconds will Cyclist A lap Cyclist B for the first time (i.e., be exactly one full lap ahead)?

Accepted Answer

Step 1: When both travel in the same direction, relative speed = 15 - 10 = 5 m/s. Step 2: For A to lap B, A must cover one full lap more than B, which means A must gain 600 m on B. Step 3: Time = Distance ÷ Relative speed = 600 ÷ 5 = 120 seconds.

Question 2

A car travels from City P to City Q (240 km apart) at a constant speed. On the return journey, it travels 20 km/h faster. If the total time for both journeys is 11 hours, what is the speed of the car from P to Q?

Accepted Answer

Step 1: Let speed from P to Q = x km/h. Then return speed = (x + 20) km/h. Step 2: Time from P to Q = 240/x hours. Time from Q to P = 240/(x+20) hours. Step 3: Total time: 240/x + 240/(x+20) = 11. Step 4: Multiply through by x(x+20): 240(x+20) + 240x = 11x(x+20). Step 5: 240x + 4800 + 240x = 11x² + 220x. Step 6: 480x + 4800 = 11x² + 220x. Step 7: 11x² - 260x - 4800 = 0. Step 8: Using quadratic formula or factoring: (11x + 120)(x - 40) = 0. Since x > 0, x = 40 km/h.

Question 3

Two runners, P and Q, run on a 400 m circular track. P runs at 8 m/s and Q at 6 m/s, both starting from the same point in the same direction. How many times will P lap Q before P completes 10 full laps?

Accepted Answer

Step 1: P completes 10 laps = 10 × 400 = 4000 m. Time taken by P = 4000 ÷ 8 = 500 seconds. Step 2: In 500 seconds, Q covers = 6 × 500 = 3000 m = 7.5 laps. Step 3: P completes 10 laps while Q completes 7.5 laps. Step 4: Number of times P laps Q = 10 - 7.5 = 2.5 laps gained. Step 5: Since one lap = 400 m, P laps Q every 400 ÷ (8-6) = 200 seconds. Step 6: In 500 seconds, number of laps = 500 ÷ 200 = 2.5. Since we count complete lappings, P laps Q exactly 2 times (at 200 s and 400 s), with a partial lap at 500 s.

Question 4

Two cyclists start from the same point and travel in opposite directions. Cyclist P travels at 12 km/h and Cyclist Q 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. Step 2: Relative speed = 12 + 18 = 30 km/h. Step 3: Time = Distance ÷ Relative speed = 90 ÷ 30 = 3 hours.

Question 5

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?

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 and Downstream speed = b + c = 12. Step 3: Adding both equations: 2b = 20, so b = 10 km/h.

Question 6

A person walks at 4 km/h and runs at 8 km/h. If the person covers a certain distance by walking for 2 hours and then running for 1 hour, what is the total distance covered?

Accepted Answer

Step 1: Distance covered while walking = Speed × Time = 4 × 2 = 8 km. Step 2: Distance covered while running = Speed × Time = 8 × 1 = 8 km. Step 3: Total distance = 8 + 8 = 16 km.

Question 7

A boat travels upstream at 15 km/h and downstream at 25 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 km/h and the speed of the current be C km/h. Upstream speed: B - C = 15. Downstream speed: B + C = 25. Step 2: Add both equations: 2B = 40, so B = 20 km/h.

Question 8

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, 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 = 500 ÷ 100 = 5 hours. Therefore, the answer is 5 hours.

Question 9

Two runners start from the same point on a circular track of 400 m. Runner A runs at 8 m/s and Runner B runs at 6 m/s in the same direction. After how much time will Runner A lap Runner B (i.e., be exactly 400 m ahead)?

Accepted Answer

Step 1: When one runner laps another on a circular track, the faster runner must cover exactly one full lap (400 m) more than the slower runner. Step 2: Relative speed = 8 - 6 = 2 m/s. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds.

Question 10

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 much time will they be 90 km apart?

Accepted Answer

Step 1: When two objects move in opposite directions from the same point, 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.

Question 11

A car is chasing a motorcycle on the same road. The car travels at 80 km/h and the motorcycle travels at 50 km/h. If the motorcycle is currently 90 km ahead, how long will it take for the car to catch up?

Accepted Answer

Step 1: When one object chases another in the same direction, relative speed is the difference of their speeds. Relative speed = 80 - 50 = 30 km/h. Step 2: Time = Distance ÷ Relative Speed = 90 ÷ 30 = 3 hours.

Question 12

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.

Question 13

A man walks at 5 km/h and a woman walks at 3 km/h. They start from the same point and walk in the same direction. After 2 hours, the man stops and waits. How much longer will the woman take to catch up to where the man stopped?

Accepted Answer

Step 1: Distance covered by the man in 2 hours = 5 × 2 = 10 km. Step 2: When the man stops, the woman is at a distance of 3 × 2 = 6 km. Step 3: The woman needs to cover the remaining distance = 10 − 6 = 4 km. Step 4: Time taken by the woman to cover 4 km at 3 km/h = 4 ÷ 3 = 1.33 hours or 1 hour 20 minutes. Therefore, the answer is 1 hour 20 minutes (or 4/3 hours).

Question 14

A boat travels upstream at 12 km/h and downstream at 20 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 km/h and the speed of the current be C km/h. Upstream speed = B − C = 12 km/h. Downstream speed = B + C = 20 km/h. Step 2: Adding both equations: (B − C) + (B + C) = 12 + 20, so 2B = 32, therefore B = 16 km/h. The speed of the boat in still water is 16 km/h.

Question 15

Two cyclists start from the same point and cycle in opposite directions. Cyclist P cycles at 15 km/h and Cyclist Q cycles at 25 km/h. After how much time will they be 120 km apart?

Accepted Answer

Step 1: When two objects move in opposite directions, relative speed is the sum of their speeds. Relative speed = 15 + 25 = 40 km/h. Step 2: Time = Distance ÷ Relative Speed = 120 ÷ 40 = 3 hours. Therefore, the answer is 3 hours.

Question 16

A car and a motorcycle are travelling in the same direction on a highway. The car travels at 80 km/h and the motorcycle at 50 km/h. If the motorcycle is 90 km ahead of the car, how long will it take for the car to catch up?

Accepted Answer

Step 1: When both objects move in the same direction, relative speed is the difference of their speeds. Relative speed = 80 − 50 = 30 km/h. Step 2: Time = Distance ÷ Relative Speed = 90 ÷ 30 = 3 hours. Therefore, the answer is 3 hours.

Question 17

Two runners start a race from the same point. Runner A runs at 12 m/s and Runner B runs at 8 m/s in the same direction. How far ahead will Runner A be after 15 seconds?

Accepted Answer

Step 1: When both runners move in the same direction, the distance between them increases at the rate of their relative speed. Relative speed = 12 − 8 = 4 m/s. Step 2: Distance covered in 15 seconds = Relative speed × Time = 4 × 15 = 60 metres. Therefore, Runner A will be 60 metres ahead.

Question 18

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. Step 2: Relative speed = 60 + 40 = 100 km/h. Step 3: Time = Distance ÷ Relative speed = 150 ÷ 100 = 1.5 hours.

Question 19

A man walks at 5 km/h and a boy runs at 8 km/h in the same direction on a straight road. If the boy is currently 9 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 is the difference of their speeds. Step 2: Relative speed = 8 - 5 = 3 km/h. Step 3: Time = Distance ÷ Relative speed = 9 ÷ 3 = 3 hours.

Question 20

A man can row 8 km/h in still water. If he rows upstream for 2 hours and covers 12 km, what is the speed of the current?

Accepted Answer

Step 1: Upstream speed = Distance ÷ Time = 12 ÷ 2 = 6 km/h. Step 2: Upstream speed = Boat speed - Current speed. So, 6 = 8 - c, where c is current speed. Step 3: c = 8 - 6 = 2 km/h.

Question 21

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 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 22

A man walks at 4 km/h and a woman walks at 6 km/h. They start from the same point and walk in the same direction. After the woman has walked for 2 hours, the man starts walking. How long will it take for the man to catch up with the woman?

Accepted Answer

Step 1: The woman walks for 2 hours at 6 km/h, covering 6 × 2 = 12 km. Step 2: When the man starts, the woman is 12 km ahead. Step 3: For the man to catch up, he must be faster. Assuming the man walks at 6 km/h (correcting the likely intent), relative speed = 6 − 4 = 2 km/h. Step 4: Time for man to catch up = 12 ÷ 2 = 6 hours. Therefore, the answer is 6 hours.

Question 23

Two runners, P and Q, run on a 600-metre circular track. P runs at 8 m/s and Q runs at 5 m/s in the same direction. How many times will P lap Q (i.e., lap from behind) in 10 minutes?

Accepted Answer

Step 1: Relative speed of P with respect to Q = 8 − 5 = 3 m/s. Step 2: Time duration = 10 minutes = 600 seconds. Step 3: Distance covered by P relative to Q in 600 seconds = 3 × 600 = 1800 metres. Step 4: Number of times P laps Q = Relative distance ÷ Track length = 1800 ÷ 600 = 3 times. Therefore, P will lap Q 3 times in 10 minutes.

RRB NTPC Relative Speed

RRB NTPC 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