Question 1

A train travels at 72 km/h. How long will it take to cover 360 km?

Accepted Answer

Step 1: Use the formula Time = Distance ÷ Speed. Step 2: Time = 360 ÷ 72 = 5 hours. Therefore, the train takes 5 hours to cover 360 km.

Question 2

A train 150 metres long passes a stationary pole in 6 seconds. What is the speed of the train in m/s?

Accepted Answer

Step 1: When a train passes a pole, the distance covered equals the length of the train = 150 metres. Step 2: Use Speed = Distance ÷ Time = 150 ÷ 6 = 25 m/s. Therefore, the speed of the train is 25 m/s.

Question 3

A train travels 240 km in 4 hours at a constant speed. What is the speed of the train in km/h?

Accepted Answer

Step 1: Use the formula Speed = Distance ÷ Time. Step 2: Speed = 240 ÷ 4 = 60 km/h. Therefore, the speed of the train is 60 km/h.

Question 4

A train covers 180 km in 3 hours. How much distance will it cover in 7 hours at the same speed?

Accepted Answer

Step 1: Find the speed using Speed = Distance ÷ Time = 180 ÷ 3 = 60 km/h. Step 2: Find distance for 7 hours using Distance = Speed × Time = 60 × 7 = 420 km. Therefore, the train covers 420 km in 7 hours.

Question 5

Two trains are moving towards each other. Train A travels at 50 km/h and Train B travels at 40 km/h. If they are initially 270 km apart, in how many hours will they meet?

Accepted Answer

Step 1: When trains move towards each other, their relative speed = Speed of A + Speed of B = 50 + 40 = 90 km/h. Step 2: Time to meet = Distance ÷ Relative Speed = 270 ÷ 90 = 3 hours. Therefore, the trains will meet in 3 hours.

Question 6

A train 200 metres long crosses a platform 400 metres long in 12 seconds. What is the speed of the train in m/s?

Accepted Answer

Step 1: When a train crosses a platform, the total distance covered = Length of train + Length of platform = 200 + 400 = 600 metres. Step 2: Speed = Distance ÷ Time = 600 ÷ 12 = 50 m/s. Therefore, the speed of the train is 50 m/s.

Question 7

Two trains start from the same station at the same time. Train M travels at 72 km/h and Train N travels at 54 km/h, both in the same direction. After 5 hours, how far apart will they be?

Accepted Answer

Step 1: Relative speed = 72 − 54 = 18 km/h (since they travel in the same direction). Step 2: Distance apart after 5 hours = Relative speed × Time = 18 × 5 = 90 km.

Question 8

A train travels 240 km from City A to City B at an average speed of 60 km/h. On the return journey, due to maintenance work, the train travels at 40 km/h. What is the average speed of the train for the entire journey (both ways)?

Accepted Answer

Step 1: Calculate time taken from A to B: Distance = 240 km, Speed = 60 km/h. Time = Distance/Speed = 240/60 = 4 hours. Step 2: Calculate time taken from B to A: Distance = 240 km, Speed = 40 km/h. Time = 240/40 = 6 hours. Step 3: Calculate average speed for entire journey. Total distance = 240 + 240 = 480 km. Total time = 4 + 6 = 10 hours. Average speed = Total distance/Total time = 480/10 = 48 km/h. Therefore, the average speed for the entire journey is 48 km/h.

Question 9

Train A of length 150 m crosses a stationary platform in 15 seconds. Train B of length 100 m travels at twice the speed of Train A. How long will Train B take to cross the same platform?

Accepted Answer

Step 1: Find speed of Train A. Distance = Length of train + Platform length. For a platform, we assume negligible length, so distance ≈ 150 m. Speed of A = 150 ÷ 15 = 10 m/s. Step 2: Speed of Train B = 2 × 10 = 20 m/s. Step 3: Train B must cover its own length (100 m) to cross the platform. Time = 100 ÷ 20 = 5 seconds.

Question 10

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A to B at 60 km/h, and Train Y travels from B to A at 40 km/h. After how many hours will they meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = sum of individual speeds. Relative speed = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 360 ÷ 100 = 3.6 hours.

Question 11

A train 200 m long takes 20 seconds to pass a man standing on the platform. How long will it take to cross a bridge of length 400 m?

Accepted Answer

Step 1: When a train passes a man (point object), distance covered = length of train = 200 m. Speed = 200 ÷ 20 = 10 m/s. Step 2: To cross a bridge, the train must cover distance = length of train + length of bridge = 200 + 400 = 600 m. Step 3: Time = 600 ÷ 10 = 60 seconds.

Question 12

Train P and Train Q are running on parallel tracks in the same direction. Train P (length 120 m) runs at 80 km/h, and Train Q (length 80 m) runs at 60 km/h. How long will Train P take to completely overtake Train Q?

Accepted Answer

Step 1: When trains move in the same direction, relative speed = difference of speeds = 80 − 60 = 20 km/h. Step 2: Convert to m/s: 20 km/h = 20 × (5/18) = 50/9 m/s ≈ 5.56 m/s. Step 3: For complete overtaking, distance to cover = sum of lengths = 120 + 80 = 200 m. Step 4: Time = 200 ÷ (50/9) = 200 × (9/50) = 36 seconds.

Question 13

A train travels 240 km in 4 hours. If the train increases its speed by 20 km/h, how much time will it take to cover the same distance?

Accepted Answer

Step 1: Original speed = 240 ÷ 4 = 60 km/h. Step 2: New speed = 60 + 20 = 80 km/h. Step 3: Time at new speed = 240 ÷ 80 = 3 hours.

Question 14

Two runners, A and B, start running simultaneously from the same point on a circular track of length 400 m. A runs at 8 m/s and B runs at 5 m/s in the same direction. After how much time will A meet B again for the first time after the start?

Accepted Answer

Step 1: Since both runners move in the same direction on a circular track, A will meet B again when A completes exactly one full lap more than B.

Step 2: Relative speed = Speed of A - Speed of B = 8 - 5 = 3 m/s

Step 3: For A to lap B (gain one complete lap), the relative distance to be covered = Length of track = 400 m

Step 4: Time = Relative Distance / Relative Speed = 400 / 3 = 133.33 seconds

Step 5: Convert to mixed number: 133.33 = 133⅓ seconds = 400/3 seconds ≈ 133 seconds (approximately)

Alternatively: Time = 400/3 = 133⅓ seconds ≈ 2 minutes 13⅓ seconds

Therefore, A will meet B again after 400/3 seconds or approximately 133⅓ seconds.

Question 15

A boat travels 36 km downstream in 2 hours and returns the same distance upstream in 3 hours. What is the speed of the stream?

Accepted Answer

Step 1: Downstream speed = 36/2 = 18 km/h. Step 2: Upstream speed = 36/3 = 12 km/h. Step 3: Speed of stream = (Downstream speed − Upstream speed) / 2 = (18 − 12) / 2 = 6/2 = 3 km/h. Therefore, the speed of the stream is 3 km/h.

Question 16

Train P and Train Q are 300 m and 200 m long respectively. They are moving in the same direction on parallel tracks at speeds of 80 km/h and 50 km/h respectively. How long will it take for train P to completely overtake train Q?

Accepted Answer

Step 1: Since trains move in the same direction, relative speed = 80 − 50 = 30 km/h. Step 2: Convert to m/s: 30 × (5/18) = 30 × 0.278 = 8.33 m/s (or 25/3 m/s). Step 3: For complete overtaking, distance to cover = Length of P + Length of Q = 300 + 200 = 500 m. Step 4: Time = Distance ÷ Relative speed = 500 ÷ (25/3) = 500 × (3/25) = 60 seconds. Therefore, train P takes 60 seconds to completely overtake train Q.

Question 17

A train travelling at 90 km/h crosses a man standing on a platform in 8 seconds. The same train crosses a bridge in 35 seconds. What is the length of the bridge?

Accepted Answer

Step 1: Convert train speed to m/s: 90 × (5/18) = 25 m/s. Step 2: Length of train = Speed × Time to cross man = 25 × 8 = 200 m. Step 3: When crossing the bridge, total distance = Length of train + Length of bridge. Time to cross bridge = (Length of train + Length of bridge) ÷ Speed. Step 4: 35 = (200 + Length of bridge) ÷ 25. Step 5: 200 + Length of bridge = 35 × 25 = 875 m. Step 6: Length of bridge = 875 − 200 = 675 m. Therefore, the bridge is 675 m long.

Question 18

Two trains start from the same station at the same time. Train A travels at 72 km/h and Train B travels at 54 km/h in the same direction. After 5 hours, Train A reduces its speed to 60 km/h. How far apart will the two trains be after a total of 8 hours from the start?

Accepted Answer

Step 1: For the first 5 hours, relative speed = 72 − 54 = 18 km/h. Distance covered by A in 5 hours = 72 × 5 = 360 km. Distance covered by B in 5 hours = 54 × 5 = 270 km. Gap after 5 hours = 360 − 270 = 90 km. Step 2: After 5 hours, Train A's speed becomes 60 km/h. Remaining time = 8 − 5 = 3 hours. Step 3: In the next 3 hours, relative speed = 60 − 54 = 6 km/h. Additional gap = 6 × 3 = 18 km. Step 4: Total gap = 90 + 18 = 108 km. Therefore, the trains are 108 km apart after 8 hours.

Question 19

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 20

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.

RRB NTPC Time, Speed & Distance Questions

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