Question 1

Two trains are running towards each other on parallel tracks. Train A is moving at 60 km/h and Train B is moving at 40 km/h. If they are currently 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. Therefore, the trains will meet in 5 hours.

Question 2

Two trains are running towards each other on parallel tracks. Train A is moving at 60 km/h and Train B is moving at 40 km/h. If they are currently 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. Therefore, the trains will meet in 5 hours.

Question 3

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = 48 ÷ 3 = 16 km/h. Step 2: Upstream speed = 48 ÷ 6 = 8 km/h. Step 3: Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2 = (16 + 8) ÷ 2 = 12 km/h. Therefore, the answer is 12 km/h.

Question 4

Train A of length 150 m crosses a stationary platform in 15 seconds. What is the speed of Train A in km/h?

Accepted Answer

Step 1: When a train crosses a platform, it travels a distance equal to its own length. Distance = 150 m, Time = 15 seconds. Step 2: Speed = Distance ÷ Time = 150 ÷ 15 = 10 m/s. Step 3: Convert m/s to km/h by multiplying by 3.6: 10 × 3.6 = 36 km/h.

Question 5

Two runners, A and B, start running simultaneously from the same point on a circular track of length 400 metres. A runs at 8 m/s and B runs at 6 m/s in the same direction. After how many seconds will A lap B for the first time (i.e., A will be exactly one full lap ahead of B)?

Accepted Answer

Step 1: When two objects move in the same direction on a circular track, the faster one laps the slower one when the difference in distances covered equals the track length. Step 2: Relative speed = 8 − 6 = 2 m/s. Step 3: Time to lap = Track length ÷ Relative speed = 400 ÷ 2 = 200 seconds.

Question 6

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

Accepted Answer

Step 1: When two objects move in the same direction on a circular track, the relative speed is the difference of their speeds. Relative speed = 8 − 6 = 2 m/s. Step 2: For A to lap B, A must gain a distance equal to the track length (400 m) on B. Step 3: Time = Distance ÷ Relative Speed = 400 ÷ 2 = 200 seconds. Therefore, the answer is 200 seconds.

Question 7

A boat travels 36 km downstream in 2 hours and the speed of the stream is 3 km/h. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = Distance / Time = 36 / 2 = 18 km/h. Step 2: Downstream speed = Boat speed + Stream speed → 18 = Boat speed + 3. Step 3: Boat speed = 18 - 3 = 15 km/h. Therefore, the answer is 15 km/h.

Question 8

Train A of length 150 m crosses a stationary platform in 15 seconds. What is the speed of Train A in km/h?

Accepted Answer

Step 1: The train crosses the platform means it travels a distance equal to its own length. Distance = 150 m, Time = 15 seconds. Step 2: Speed in m/s = Distance ÷ Time = 150 ÷ 15 = 10 m/s. Step 3: Convert to km/h by multiplying by 3.6 (or 18/5): 10 × 3.6 = 36 km/h.

Question 9

A train travels 288 km in 4 hours. What is its speed in metres per second?

Accepted Answer

Step 1: Calculate speed in km/h using Speed = Distance ÷ Time. Speed = 288 ÷ 4 = 72 km/h. Step 2: Convert km/h to m/s by multiplying by 5/18. Speed = 72 × (5/18) = 360/18 = 20 m/s. Therefore, the answer is 20 m/s.

Question 10

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. What is the speed of the boat in still water?

Accepted Answer

Step 1: Downstream speed = 48 ÷ 3 = 16 km/h. Step 2: Upstream speed = 48 ÷ 6 = 8 km/h. Step 3: Speed of boat in still water = (Downstream speed + Upstream speed) ÷ 2 = (16 + 8) ÷ 2 = 12 km/h. Therefore, the answer is 12 km/h.

Question 11

Two trains A and B start simultaneously from opposite ends of a 360 km track. Train A travels at 60 km/h and Train B travels at 90 km/h. After 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 + 90 = 150 km/h

Step 2: Use the formula: Time = Distance / Relative Speed
Time = 360 / 150 = 2.4 hours

Step 3: Converting to hours and minutes: 2.4 hours = 2 hours 24 minutes
Or in decimal form: 2.4 hours

Therefore, the trains will meet after 2.4 hours (or 2 hours 24 minutes).

Question 12

A train travels 240 km at a speed of 60 km/h. If the same train then travels 180 km at a speed of 45 km/h, what is the average speed for the entire journey?

Accepted Answer

Step 1: Calculate time for first part: Distance = 240 km, Speed = 60 km/h, Time₁ = 240/60 = 4 hours. Step 2: Calculate time for second part: Distance = 180 km, Speed = 45 km/h, Time₂ = 180/45 = 4 hours. Step 3: Total distance = 240 + 180 = 420 km. Total time = 4 + 4 = 8 hours. Step 4: Average speed = Total distance / Total time = 420/8 = 52.5 km/h. Therefore, the answer is 52.5 km/h.

Question 13

A train travels a distance of 360 km in 4 hours. What is the speed of the train in metres per second?

Accepted Answer

Step 1: Speed in km/h = 360 ÷ 4 = 90 km/h. Step 2: Convert to m/s using the formula: speed (m/s) = speed (km/h) × (5/18). Step 3: 90 × (5/18) = 450/18 = 25 m/s. Therefore, the answer is 25 m/s.

Question 14

A boat travels 48 km downstream in 3 hours and 48 km upstream in 6 hours. A man swims at a constant speed in still water. What is the speed of the current?

Accepted Answer

Step 1: Downstream speed = 48 ÷ 3 = 16 km/h. Step 2: Upstream speed = 48 ÷ 6 = 8 km/h. Step 3: Speed of current = (Downstream speed − Upstream speed) ÷ 2 = (16 − 8) ÷ 2 = 4 km/h. Therefore, the answer is 4 km/h.

Question 15

A train travels 240 km in 4 hours at constant speed. If it needs to cover an additional 180 km at the same speed, how much total time (in hours) will it take to complete the entire journey of 420 km?

Accepted Answer

Step 1: Calculate the train's speed from the first part of the journey: Speed = Distance ÷ Time = 240 ÷ 4 = 60 km/h. Step 2: Calculate total time for the entire 420 km journey: Time = Total Distance ÷ Speed = 420 ÷ 60 = 7 hours. Therefore, the answer is 7 hours.

Question 16

Two trains start simultaneously from stations A and B, which are 360 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. At what time will they meet, and how far will Train X have travelled by then?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = sum of individual speeds = 60 + 90 = 150 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 360 ÷ 150 = 2.4 hours. Step 3: Distance travelled by Train X = Speed of X × Time = 60 × 2.4 = 144 km. Therefore, the answer is 144 km.

Question 17

Two trains, A and B, start simultaneously from stations X and Y respectively, which are 480 km apart. Train A travels towards Y at 60 km/h, while train B travels towards X at 40 km/h. After how many hours will they meet, and at what distance from station X?

Accepted Answer

Step 1: When two trains travel towards each other, their relative speed = 60 + 40 = 100 km/h. Step 2: Time to meet = Total distance ÷ Relative speed = 480 ÷ 100 = 4.8 hours. Step 3: Distance from X where they meet = Speed of A × Time = 60 × 4.8 = 288 km. Therefore, they meet after 4.8 hours at 288 km from station X.

Question 18

Two trains start simultaneously from stations A and B, which are 360 km apart. Train X travels from A to B at 80 km/h, while Train Y travels from B to A at 100 km/h. At what distance from station A will the two trains meet?

Accepted Answer

Step 1: When two objects move towards each other, their relative speed = Sum of individual speeds = 80 + 100 = 180 km/h.

Step 2: Time taken to meet = Total distance / Relative speed = 360 / 180 = 2 hours.

Step 3: Distance covered by Train X from station A in 2 hours = Speed × Time = 80 × 2 = 160 km.

Therefore, the trains will meet at 160 km from station A.

Question 19

A train travels 240 km in 4 hours at constant speed. If it needs to cover the same distance in 3 hours, by what percentage must its speed be increased?

Accepted Answer

Step 1: Original speed = 240 ÷ 4 = 60 km/h. Step 2: Required speed = 240 ÷ 3 = 80 km/h. Step 3: Speed increase = 80 − 60 = 20 km/h. Step 4: Percentage increase = (20 ÷ 60) × 100 = 33.33% or 33⅓%. Therefore, the answer is 33⅓%.

Question 20

A boat travels 48 km downstream in 3 hours and 48 km upstream in 4 hours. A man swims at a constant speed in still water. If the man swims the same 48 km downstream, how long will it take him (in hours)?

Accepted Answer

Step 1: Find downstream speed of boat: 48 ÷ 3 = 16 km/h. Step 2: Find upstream speed of boat: 48 ÷ 4 = 12 km/h. Step 3: Use formulas: Downstream = b + s, Upstream = b − s, where b = boat speed in still water, s = stream speed. So 16 = b + s and 12 = b − s. Step 4: Adding equations: 28 = 2b, so b = 14 km/h. Step 5: Subtracting: 4 = 2s, so s = 2 km/h. Step 6: Man's speed in still water = boat's speed in still water = 14 km/h (given constant speed in still water). Step 7: Man's downstream speed = 14 + 2 = 16 km/h. Step 8: Time = 48 ÷ 16 = 3 hours.

SSC CGL Time, Speed & Distance Questions

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