Question 1

A 600 m long train is moving at 67 km/h and overtakes a man walking at 7 km/h in the same direction of the train. How many seconds does the train take to completely cross the man?

Accepted Answer

Introduction / Context: This numerical aptitude question involves a train overtaking a man walking in the same direction. It tests the concept of relative speed when two objects move along the same line in the same direction and asks for the time taken to completely cross the man. Given Data / Assumptions: Length of the train = 600 m. Speed of the train = 67 km/h. Speed of the man = 7 km/h. They move in the same direction along the track. We assume constant speeds and straight track. Concept / Approach: When two objects move in the same direction, the effective relative speed is the difference of their speeds. The train needs to cover a distance equal to its own length relative to the man in order to completely cross him. We convert speeds from km/h to m/s, compute the relative speed, and then use time = distance / speed to find the crossing time in seconds. Step-by-Step Solution: Step 1: Relative speed in km/h = 67 - 7 = 60 km/h. Step 2: Convert 60 km/h to m/s using factor 5/18. Step 3: Relative speed = 60 * 5 / 18 = 50 / 3 m/s. Step 4: Distance to be covered relative to the man = length of train = 600 m. Step 5: Use time = distance / speed, so time = 600 / (50 / 3). Step 6: Time = 600 * 3 / 50 = 1800 / 50 = 36 seconds. Verification / Alternative check: Check using a quick mental method. Relative speed 50 / 3 m/s is approximately 16.67 m/s. If time were 36 seconds, distance covered would be 16.67 * 36, which is very close to 600 m, matching the train length. This confirms that the train needs 36 seconds to completely cross the man. Why Other Options Are Wrong: 29 seconds: At this time, distance covered would be less than 600 m, so the train would not have fully passed the man. 58 seconds: This time is too large and would imply the train has travelled much more than its own length relative to the man. 44 seconds: This is also larger than necessary and does not match the exact distance calculation. Common Pitfalls: Typical mistakes include adding the speeds instead of subtracting them for motion in the same direction and forgetting to convert km/h into m/s. Another common error is to use the total path length instead of the train length when a train is crossing a man or pole, where only the train length matters. Final Answer: The train takes 36 seconds to cross the man completely.

Question 2

A jogger runs at 9 km/h alongside a railway track and is 240 m ahead of the engine of a 120 m long train that is moving in the same direction at 45 km/h. In how many seconds will the train completely pass the jogger?

Accepted Answer

Introduction / Context: This train and jogger question checks understanding of relative speed in the same direction and the idea that a train must cover both the initial gap and its own length to completely pass a moving person. It is a common pattern in competitive exam aptitude sections on trains and distances. Given Data / Assumptions: Speed of jogger = 9 km/h. Speed of train = 45 km/h. Length of train = 120 m. Jogger is initially 240 m ahead of the train engine. Both move in the same direction at constant speeds. Concept / Approach: The train must first close the 240 m gap between the engine and the jogger, and then cover its own length of 120 m to pass completely. Since both move in the same direction, effective relative speed is the difference of their speeds. We convert this relative speed into metres per second and use time = distance / speed to find the time taken to pass the jogger. Step-by-Step Solution: Step 1: Relative speed in km/h = 45 - 9 = 36 km/h. Step 2: Convert 36 km/h to m/s using factor 5/18. Step 3: Relative speed = 36 * 5 / 18 = 10 m/s. Step 4: Total distance to be covered relative to jogger = initial gap + train length = 240 + 120 = 360 m. Step 5: Use time = distance / speed, so time = 360 / 10 = 36 seconds. Verification / Alternative check: We can check by seeing how far each moves in 36 seconds. Train distance = 10 m/s relative speed * 36 s = 360 m compared to jogger, which matches the required distance 360 m. This shows that the front of the train reaches and then fully clears the jogger in 36 seconds at the given speeds. Why Other Options Are Wrong: 10 seconds: At 10 seconds, the relative distance covered is only 100 m, which is less than the 360 m needed. 48 seconds: This would give 480 m of relative motion, which is beyond the required distance. 56 seconds: This is even longer and gives a relative distance of 560 m, which is not consistent with the described situation. Common Pitfalls: One common mistake is to consider only the 240 m gap and forget that the whole length of the train must clear the jogger. Another error is to add speeds incorrectly or fail to convert km/h to m/s. Some learners also confuse relative distance with absolute distance along the track, so it is important to think carefully in terms of positions relative to the jogger. Final Answer: The train will completely pass the jogger in 36 seconds.

Question 3

Train A crosses a man standing on a platform in 8 seconds and crosses a 180 m long platform P in 17 seconds. If Train A crosses Train B, which is coming from the opposite direction at 108 km/h, in 8 seconds, then how much time (in seconds) will Trai…

Accepted Answer

Introduction / Context: This is a multi step trains question involving the length and speed of one train, the length of a platform, and the relative speed when another train comes from the opposite direction. We must first determine the speed and length of Train A, then use the crossing time with Train B to find the length of Train B, and finally calculate how long Train B will take to cross the same platform P. Given Data / Assumptions: Train A crosses a man in 8 seconds. Train A crosses a platform of length 180 m in 17 seconds. Train A crosses Train B in 8 seconds when Train B runs in the opposite direction at 108 km/h. We assume constant speeds for both trains. Train B must cross the same 180 m platform completely. Concept / Approach: When a train crosses a man, the distance is just the length of the train. When it crosses a platform, the distance is the sum of the train length and platform length. From these, we can find Train A speed and length. Then we use relative speed for opposite directions to find Train B length based on the time taken to cross each other. Finally, we use Train B speed and its length plus platform length to compute the time required to cross platform P. Step-by-Step Solution: Step 1: Let length of Train A be LA metres and its speed be vA m/s. Step 2: From crossing a man, LA / vA = 8, so LA = 8 * vA. Step 3: From crossing a 180 m platform in 17 seconds, (LA + 180) / vA = 17. Step 4: Substitute LA = 8 * vA into LA + 180 = 17 * vA, giving 8 * vA + 180 = 17 * vA. Step 5: Simplify to 180 = 9 * vA, so vA = 20 m/s. Step 6: Then length of Train A = LA = 8 * 20 = 160 m. Step 7: Speed of Train B = 108 km/h = 108 * 5 / 18 = 30 m/s. Step 8: Relative speed when trains move in opposite directions = 20 + 30 = 50 m/s. Step 9: Let length of Train B be LB. Time to cross each other is 8 seconds, so (LA + LB) / 50 = 8. Step 10: This gives LA + LB = 400, so LB = 400 - 160 = 240 m. Step 11: For Train B crossing platform P, distance = LB + 180 = 240 + 180 = 420 m. Step 12: Time = distance / speed = 420 / 30 = 14 seconds. Verification / Alternative check: We can quickly check each piece. Train A speed 20 m/s gives length 160 m from LA = vA * 8. Crossing a 180 m platform gives total distance 340 m, and 340 / 20 = 17 seconds, matching the data. For Train B, length 240 m with Train A in opposite direction: total length 400 m, relative speed 50 m/s, time 400 / 50 = 8 seconds, also correct. Finally, Train B crossing 180 m platform means 420 m at 30 m/s, confirming 14 seconds. Why Other Options Are Wrong: 16 seconds: Would imply total distance 480 m, not 420 m, for the given speed of Train B. 11 seconds: Leads to unrealistically short distance and contradicts the derived length of Train B. 12 seconds: Gives distance 360 m which is less than LB + platform length. Common Pitfalls: Learners may mix up which train length is used in which step or forget that crossing a man only involves the train length. Some also incorrectly use the difference instead of the sum of speeds when trains move in opposite directions. It is also easy to misinterpret times or skip the step of converting units from km/h to m/s when needed, although here Train A speed was directly found in m/s from the time relationships. Final Answer: Train B will take 14 seconds to cross platform P.

Question 4

Two trains A and B have speeds in the ratio 5 : 8 and the sum of their lengths is 660 m. The ratio of the times they take to cross an electric pole is 4 : 3. What is the difference between the lengths (in metres) of the two trains?

Accepted Answer

Introduction / Context: This is a reasoning based trains question that connects ratios of speeds, ratios of times to cross a pole, and the sum of train lengths. It tests a candidate's ability to manipulate ratios and understand the relationship between time, distance, and speed when a train passes a fixed point like an electric pole. Given Data / Assumptions: Speed ratio of trains A and B = 5 : 8. Sum of lengths of trains A and B = 660 m. Ratio of times taken to cross a pole by A and B = 4 : 3. Each train moves at constant speed when crossing the pole. Crossing a pole means distance = train length only. Concept / Approach: Time to cross a pole is length divided by speed. Because we know the ratio of times and the ratio of speeds, we can deduce the ratio of lengths. Once we find length ratio, we use the total length to find individual lengths. Finally we compute their difference. This avoids any need to know the absolute speeds in km/h or m/s. Step-by-Step Solution: Step 1: Let speeds be 5k and 8k for trains A and B. Step 2: Let lengths be LA and LB. Step 3: Time to cross a pole for A is TA = LA / (5k). Step 4: Time to cross a pole for B is TB = LB / (8k). Step 5: Given TA : TB = 4 : 3, so (LA / 5k) / (LB / 8k) = 4 / 3. Step 6: Simplify to (LA / LB) * (8 / 5) = 4 / 3, so LA / LB = (4 / 3) * (5 / 8) = 5 / 6. Step 7: Therefore LA : LB = 5 : 6. Step 8: Let LA = 5x and LB = 6x, with LA + LB = 660. Step 9: So 5x + 6x = 660 gives 11x = 660, and x = 60. Step 10: Then LA = 5 * 60 = 300 m and LB = 6 * 60 = 360 m. Step 11: Difference between lengths = 360 - 300 = 60 m. Verification / Alternative check: Check with times. If speeds are 5k and 8k, times are 300 / (5k) = 60 / k for A and 360 / (8k) = 45 / k for B. The time ratio TA : TB is then 60 : 45 = 4 : 3, which matches the given information. The sum of lengths is 300 + 360 = 660 m as required. So the values are correct. Why Other Options Are Wrong: 50 m or 40 m: These differences do not agree with any pair of lengths that both sum to 660 m and satisfy the time ratio 4 : 3. 45 m: Similarly, it does not fit both the total length and the required time ratio simultaneously. Common Pitfalls: Students may try to assign arbitrary speeds in km/h and convert units unnecessarily, which complicates the problem. Another pitfall is forgetting that time is directly proportional to length and inversely proportional to speed, so using ratios incorrectly leads to mistakes. Some candidates also misinterpret crossing a pole as involving additional distance beyond the train length, which is not correct. Final Answer: The difference between the lengths of the two trains is 60 m.

Question 5

A train is moving at a speed of 72 km/h. How many seconds will it take to cover a distance of 1400 m?

Accepted Answer

Introduction / Context: This is a straightforward speed, distance, and time question often seen in aptitude tests. It involves a train moving at a given speed, and we must determine how long it takes to cover a specified distance, with all units converted consistently. Given Data / Assumptions: Speed of train = 72 km/h. Distance to be covered = 1400 m. The train moves in a straight line with constant speed. We need the time in seconds. Concept / Approach: We use the fundamental formula time = distance / speed. Since the distance is given in metres and the answer is required in seconds, it is simplest to convert the speed to metres per second. Once the speed is in m/s, dividing distance in metres by speed immediately gives time in seconds. Step-by-Step Solution: Step 1: Convert speed from km/h to m/s using 1 km/h = 5/18 m/s. Step 2: Speed in m/s = 72 * 5 / 18 = 20 m/s. Step 3: Distance to be covered = 1400 m. Step 4: Use time = distance / speed, so time = 1400 / 20 seconds. Step 5: Compute 1400 / 20 = 70 seconds. Verification / Alternative check: For a quick check, note that at 20 m/s the train covers 200 m in 10 seconds. Scaling, 1400 m is 7 times 200 m, so the time is 7 times 10 seconds, which is 70 seconds. This mental check confirms the calculation without further algebra. Why Other Options Are Wrong: 80 seconds: This would correspond to an effective speed of 17.5 m/s, not 20 m/s. 72 seconds: This would imply a non exact match between the actual speed and the required distance. 84 seconds: This is even longer and clearly does not match the value computed using the correct formula. Common Pitfalls: Common errors include using distance in kilometres with speed in metres per second or forgetting to convert units at all. Some learners wrongly apply the conversion factor 18/5 instead of 5/18 when changing from km/h to m/s. Always remember that 1 km/h equals 5/18 m/s and not the reverse. Final Answer: The train will take 70 seconds to cover 1400 m.

Question 6

Train A takes 1 hour more than Train B to travel a distance of 720 km. Later, due to engine trouble, the speed of Train B decreases by one third, so that it now takes 3 hours more than Train A to cover the same 720 km. What is the speed (in km/h) of…

Accepted Answer

Introduction / Context: This is an algebra based time, speed, and distance question set in the context of trains. Train A and Train B initially cover the same long distance with a 1 hour difference in their travel times. Later the speed of Train B is reduced, changing the time relationship. We use these conditions to determine the original speed of Train A. Given Data / Assumptions: Distance for each journey = 720 km. Train A takes 1 hour more than Train B initially. Speed of Train B later becomes two thirds of its original speed. With reduced speed, Train B now takes 3 hours more than Train A to travel 720 km. Both trains travel at constant speeds during each scenario. Concept / Approach: Let vA and vB be the original speeds of Train A and Train B. Time is distance divided by speed. We set up one equation for the initial situation and another for the situation after Train B speed changes. This leads to two equations in the two unknowns vA and vB, which we solve simultaneously. Finally, we report the value of vA, the speed of Train A. Step-by-Step Solution: Step 1: Let vA be speed of Train A and vB be speed of Train B in km/h. Step 2: Initial times are tA = 720 / vA and tB = 720 / vB. Step 3: Train A takes 1 hour more, so 720 / vA = 720 / vB + 1. Step 4: After engine trouble, speed of Train B becomes (2 / 3) * vB. Step 5: New time for Train B is tB2 = 720 / ((2 / 3) * vB) = 1080 / vB. Step 6: Now Train B takes 3 hours more than Train A, so 1080 / vB = 720 / vA + 3. Step 7: Solve the system of equations: 720 / vA = 720 / vB + 1 1080 / vB = 720 / vA + 3. Step 8: Solving gives vA = 80 km/h and vB = 90 km/h. Verification / Alternative check: Check initial times: tA = 720 / 80 = 9 hours and tB = 720 / 90 = 8 hours, so Train A takes 1 hour more. After engine trouble, Train B speed is (2 / 3) * 90 = 60 km/h, so tB2 = 720 / 60 = 12 hours. Now tB2 - tA = 12 - 9 = 3 hours, which matches the problem statement. This confirms the result. Why Other Options Are Wrong: 90 km/h: This is actually the speed of Train B, not Train A. 60 km/h: This is Train B speed after the engine trouble, not the original speed of Train A. 70 km/h: Using this value for Train A does not satisfy both time conditions simultaneously. Common Pitfalls: Learners may misinterpret the phrase speed falls by a third and incorrectly use vB / 3 instead of two thirds of vB. Another common mistake is mixing up which train is slower in each scenario and setting up the time differences incorrectly. It is important to carefully define variables and write each condition as a separate equation before solving. Final Answer: The speed of Train A is 80 km/h.

Question 7

A uniformly moving train 480 m long takes 3 minutes to completely cross a platform. If the same train at the same speed takes 30 seconds to completely pass a pole, what is the length (in metres) of the platform?

Accepted Answer

Introduction / Context: This question combines two standard train scenarios. The train crosses a platform in a given time and also crosses a pole in a shorter time. Using the second situation, we can compute the train speed. Then, from the first situation, we compute the total distance travelled over the platform and finally extract the platform length. Given Data / Assumptions: Length of train = 480 m. Time to completely cross a platform = 3 minutes = 180 seconds. Time to completely cross a pole = 30 seconds. The train moves at uniform (constant) speed in both situations. Crossing a pole involves only the train length, while crossing a platform involves train length plus platform length. Concept / Approach: First, we find the speed of the train from the pole crossing data, because distance and time are simple there. Once we know the speed in metres per second, we multiply it by the time taken to cross the platform to get the total distance travelled. The total distance equals train length plus platform length. Subtracting the known train length gives the platform length. Step-by-Step Solution: Step 1: When crossing a pole, distance = train length = 480 m. Step 2: Time to cross pole = 30 seconds, so speed = distance / time = 480 / 30 m/s. Step 3: Compute speed = 16 m/s. Step 4: When crossing the platform, time = 3 minutes = 180 seconds. Step 5: Total distance covered in 180 seconds = speed * time = 16 * 180 = 2880 m. Step 6: Total distance = train length + platform length. Step 7: So 2880 = 480 + platform length. Step 8: Platform length = 2880 - 480 = 2400 m. Verification / Alternative check: We can check by recomputing times. With speed 16 m/s and platform length 2400 m, total distance when crossing platform is 480 + 2400 = 2880 m. Time = 2880 / 16 = 180 seconds, which is exactly 3 minutes. For the pole, distance is 480 m, time is 480 / 16 = 30 seconds, matching the given data. Both conditions are satisfied, so the platform length is correct. Why Other Options Are Wrong: 600 m and 1200 m: These values would make the total distance too small and the time to cross platform much less than 3 minutes at the calculated speed. 4800 m: This would give a very large total distance 5280 m and time 5280 / 16 = 330 seconds, which is far greater than 3 minutes. Common Pitfalls: A typical mistake is to treat crossing a platform the same as crossing a pole and only consider train length. Another error is mixing seconds and minutes without proper conversion. Some learners incorrectly use the 3 minutes information first, which is more complex than using the simpler pole crossing to find speed. Always use the simplest case to find speed and then move to more complicated distances. Final Answer: The length of the platform is 2400 m.

Question 8

A train covers a distance of 12 km in 10 minutes. If it takes 6 seconds to pass a telegraph post, what is the length (in metres) of the train?

Accepted Answer

Introduction / Context: This question makes you calculate the length of a train using its speed over a known distance and the time taken to cross a fixed object, a telegraph post. It is a direct application of the relationship between speed, distance, and time that frequently appears in aptitude tests on trains. Given Data / Assumptions: The train covers 12 km in 10 minutes. Time taken to pass a telegraph post = 6 seconds. Crossing a post means the distance travelled equals the length of the train. The train moves at constant speed in a straight line. Concept / Approach: From the 12 km in 10 minutes information, we can compute the speed in metres per second. After that, crossing the telegraph post is a simple distance = speed * time calculation where distance equals the train length. We convert units properly to keep everything consistent and then find the required length in metres. Step-by-Step Solution: Step 1: Convert 12 km to metres: 12 km = 12000 m. Step 2: Convert 10 minutes to seconds: 10 minutes = 600 seconds. Step 3: Speed of train in m/s = distance / time = 12000 / 600 = 20 m/s. Step 4: When crossing a telegraph post, distance travelled during the crossing time is equal to length of train. Step 5: Time to cross the post = 6 seconds. Step 6: Train length = speed * time = 20 * 6 = 120 m. Verification / Alternative check: We can recheck the logic quickly. A train that travels 12 km in 10 minutes indeed moves at 72 km/h, which converts to 72 * 5 / 18 = 20 m/s. Using 20 m/s for 6 seconds gives 120 m, which is a reasonable length for a train. The calculations match at each step, confirming the result. Why Other Options Are Wrong: 90 m and 100 m: These are too short for a train moving 20 m/s over 6 seconds, and give times or distances that do not match the given data. 140 m: This implies the train would need 7 seconds at 20 m/s, not 6 seconds, to pass the telegraph post. Common Pitfalls: Errors usually arise from improper unit conversions, such as forgetting to convert minutes to seconds or kilometres to metres. Some learners also mistakenly treat the 12 km as the train length rather than a distance used only for speed calculation. Keeping units consistent and remembering that a fixed post involves only the entire train length is crucial. Final Answer: The length of the train is 120 m.

Question 9

A passenger train running at 80 km/h leaves a railway station 6 hours after a goods train has departed and overtakes the goods train in 4 hours. What is the speed (in km/h) of the goods train?

Accepted Answer

Introduction / Context: This problem involves two trains moving in the same direction on a straight railway track. A slower goods train starts first, followed by a faster passenger train that eventually overtakes it. We use the idea of relative speed and head start distance to calculate the speed of the goods train. Given Data / Assumptions: Speed of passenger train = 80 km/h. Goods train leaves first. Passenger train leaves the station 6 hours later. Passenger train overtakes the goods train in 4 hours after its own departure. Both trains travel at constant speeds along the same direction. Concept / Approach: Let the speed of the goods train be v km/h. The goods train travels for 10 hours by the time they meet, while the passenger train travels for 4 hours. Since they meet at the same point, the distances covered by both trains must be equal. This leads to a linear equation in v, which we solve to obtain the required speed. Step-by-Step Solution: Step 1: Let v be the speed of the goods train in km/h. Step 2: Time travelled by goods train until overtaken = 6 + 4 = 10 hours. Step 3: Time travelled by passenger train until the meeting point = 4 hours. Step 4: Distance covered by goods train = v * 10 km. Step 5: Distance covered by passenger train = 80 * 4 = 320 km. Step 6: Because both reach the same point, v * 10 = 320. Step 7: Solve for v, giving v = 320 / 10 = 32 km/h. Verification / Alternative check: Check with distances. In 10 hours at 32 km/h, the goods train travels 320 km. The passenger train, in 4 hours at 80 km/h, also travels 320 km. Since both distances are equal, they indeed meet at the same position after the stated times, confirming that 32 km/h is the correct speed for the goods train. Why Other Options Are Wrong: 50 km/h: This would give 500 km for the goods train and only 320 km for the passenger train, so they would never meet in 4 hours. 45 km/h: Gives 450 km for the goods train and 320 km for the passenger, again not equal. 64 km/h: Leads to 640 km for the goods train and 320 km for the passenger train, violating the meeting condition. Common Pitfalls: Some learners incorrectly use relative speed methods without accounting for the different start times, or they forget that the total time the goods train travels is larger than the time for the passenger train. Others mistakenly try to add distances or use different reference frames. Writing a clear equation based on equal distances at the meeting point helps avoid these issues. Final Answer: The speed of the goods train is 32 km/h.

Question 10

Train A leaves station A for station B at 4 p.m. at an average speed of 80 km/h. At 8 p.m., another train leaves station A for station B on a parallel track at an average speed of 120 km/h. At what distance (in km) from station A will the second tra…

Accepted Answer

Introduction / Context: This is a classic chasing problem with two trains starting from the same station at different times but travelling at different speeds. The first train leaves earlier at a lower speed, and the faster second train starts later and eventually overtakes it. We need to find the distance from the starting station where this overtaking occurs. Given Data / Assumptions: First train (Train A) speed = 80 km/h. Second train speed = 120 km/h. Train A departs at 4 p.m. Second train departs at 8 p.m., which is 4 hours later. Both trains travel from station A towards station B on parallel tracks at constant speeds. Concept / Approach: Let T be the time in hours after 4 p.m. when the second train catches the first. Train A travels the entire T hours, while the second train travels only T minus 4 hours because it starts later. At the catching moment, the distances from A must be equal. We equate these distances to form an equation in T, solve for T, and then compute the distance from station A using Train A speed. Step-by-Step Solution: Step 1: Let T be the time in hours after 4 p.m. when the second train overtakes the first. Step 2: Distance travelled by Train A = 80 * T km. Step 3: The second train starts at 8 p.m., so its travel time is T - 4 hours. Step 4: Distance travelled by second train = 120 * (T - 4) km. Step 5: At overtaking, distances from A are equal, so 80 * T = 120 * (T - 4). Step 6: Simplify: 80T = 120T - 480, which gives 40T = 480. Step 7: Solve for T: T = 480 / 40 = 12 hours after 4 p.m. Step 8: Distance from A when they meet = 80 * 12 = 960 km. Verification / Alternative check: At T = 12 hours, time for Train A is 12 hours, and for the second train it is 12 - 4 = 8 hours. Distances are 80 * 12 = 960 km for Train A and 120 * 8 = 960 km for the second train. Both distances are equal, confirming they meet 960 km from station A. The result fully agrees with the conditions given in the question. Why Other Options Are Wrong: 900 km, 940 km, and 980 km all correspond to times that do not satisfy the relation between the travel times of the two trains and their speeds. For example, 900 km would imply T = 900 / 80 which does not work correctly when we test it in the equation 80T = 120(T - 4). Common Pitfalls: Students sometimes forget that the second train travels for fewer hours. Using the same time variable for both trains without subtracting 4 hours for the later start leads to incorrect equations. Another common error is to use relative speed directly over the entire time interval instead of considering the head start that Train A has before the second train begins its journey. Final Answer: The second train will overtake the first train 960 km from station A.

Question 11

A train travels 40 percent faster than a car. Both start from point A at the same time and reach point B, which is 140 km away, at exactly the same time. On the way, the train stops for a total of 25 minutes at stations. What is the speed (in km/h) …

Accepted Answer

Introduction / Context: This problem compares the motion of a car and a train travelling the same distance between two points. The train is faster but has stoppage time at stations. The key idea is that despite different speeds and stops, both reach the destination simultaneously. We use this time equality to determine the train speed. Given Data / Assumptions: Distance from A to B = 140 km. Train travels 40 percent faster than the car. Train stops for a total of 25 minutes. Both start together from point A and reach point B at the same moment. Speeds are constant when each vehicle is moving. Concept / Approach: Let v be the speed of the car in km/h. Then the train speed is 1.4 * v because it is 40 percent faster. Car travel time is distance divided by its speed. Train travel time has two parts: actual running time plus stoppage time. Since arrival times are equal, their total times must match. We convert stoppage time to hours, form an equation in v, solve for v, and then compute the train speed as 1.4 * v. Step-by-Step Solution: Step 1: Let speed of car be v km/h. Step 2: Speed of train = 1.4 * v km/h. Step 3: Time taken by car = 140 / v hours. Step 4: Running time of train (without stops) = 140 / (1.4 * v) hours. Step 5: Simplify running time: 140 / (1.4 * v) = 100 / v hours. Step 6: Stoppage time for train = 25 minutes = 25 / 60 hours = 5 / 12 hours. Step 7: Total time for train = 100 / v + 5 / 12 hours. Step 8: Since both reach together, 140 / v = 100 / v + 5 / 12. Step 9: Subtract: (140 / v) - (100 / v) = 5 / 12, so 40 / v = 5 / 12. Step 10: Solve for v: v = 40 * 12 / 5 = 96 km/h. Step 11: Train speed = 1.4 * 96 = 134.4 km/h. Verification / Alternative check: Car time = 140 / 96 hours which is about 1.458 hours. Train running time is 100 / 96 which is about 1.0417 hours. Adding stoppage time 5 / 12 (about 0.4167) gives 1.4584 hours, approximately equal to car time, allowing for rounding. This confirms that the train speed 134.4 km/h satisfies the condition that both arrive together. Why Other Options Are Wrong: 67 km/h: This is far too slow given that the train is faster than the car and still must make up for stoppages. 145.9 km/h and 160 km/h: These speeds would make the train arrive significantly earlier even after stopping 25 minutes, contradicting the requirement that both arrive at the same time. Common Pitfalls: A common mistake is to forget to convert stoppage time from minutes to hours or to treat the 40 percent faster condition incorrectly by adding a fixed value instead of a percentage of the car speed. Some learners also misinterpret the phrase reach at the same time and try to balance distances instead of times. Always equate total travel times when two journeys end together. Final Answer: The speed of the train is 134.4 km/h.

Question 12

A train 110 m long is running at a speed of 72 km/h. How much time (in seconds) will it take to completely cross a bridge of length 132 m?

Accepted Answer

Introduction / Context: This question involves a train passing over a bridge and asks for the time taken. It uses the standard idea that when a train crosses a bridge, the distance travelled is the sum of the train length and the bridge length, and that we must convert the speed to compatible units before applying the time formula. Given Data / Assumptions: Train length = 110 m. Bridge length = 132 m. Speed of train = 72 km/h. Train moves at constant speed throughout the crossing. Concept / Approach: We first compute the total distance the train must travel while fully crossing the bridge, which is train length plus bridge length. Then we convert the speed from km/h to m/s so that distance in metres divided by speed in metres per second gives time in seconds. This is a direct application of time = distance / speed. Step-by-Step Solution: Step 1: Total distance to be covered while crossing the bridge = 110 + 132 = 242 m. Step 2: Convert speed 72 km/h to m/s using 1 km/h = 5/18 m/s. Step 3: Speed in m/s = 72 * 5 / 18 = 20 m/s. Step 4: Use time = distance / speed, so time = 242 / 20 seconds. Step 5: Compute 242 / 20 = 12.1 seconds. Verification / Alternative check: Check by approximate reasoning. At 20 m/s, in 10 seconds the train covers 200 m, and in 2.1 seconds it covers about 42 m, giving a total of 242 m in 12.1 seconds. This matches the distance we calculated and fits the given values. Therefore the computed time is consistent and correct. Why Other Options Are Wrong: 9.8 sec: This is too short. At 20 m/s, the train would cover only 196 m in this time, less than 242 m. 12.42 sec and 14.3 sec: These are larger than the correct time. At these durations, the train would cover more than 242 m, which contradicts the requirement. Common Pitfalls: Typical mistakes include using only the train length instead of train plus bridge length, or forgetting to convert the speed properly from km/h to m/s. Some learners also misplace decimals when dividing the total distance by the speed, so it is important to compute carefully or simplify fractions before performing the division. Final Answer: The train will take 12.1 sec to cross the bridge completely.

Question 13

Two trains are moving in opposite directions at speeds of 43 km/h and 51 km/h respectively. The slower train takes 9 seconds to completely cross a man sitting in the faster train. What is the length (in metres) of the slower train?

Accepted Answer

Introduction / Context: This problem involves two trains moving in opposite directions. We focus on the perspective of a man sitting in the faster train while the slower train passes him. The key idea is that the relative speed of the trains determines how quickly the slower train passes the man, and that the distance covered in this time equals the length of the slower train. Given Data / Assumptions: Speed of slower train = 43 km/h. Speed of faster train = 51 km/h. Trains move in opposite directions. Time taken by slower train to pass the man in the faster train = 9 seconds. We assume straight track and constant speeds. Concept / Approach: From the viewpoint of the man on the faster train, the slower train appears to approach with a relative speed that is the sum of both speeds, because they move in opposite directions. Once we compute this relative speed in metres per second, we multiply it by the given time to get the distance covered, which is simply the length of the slower train since only that train is passing the man. Step-by-Step Solution: Step 1: Relative speed in km/h = 43 + 51 = 94 km/h. Step 2: Convert 94 km/h to m/s using 1 km/h = 5/18 m/s. Step 3: Relative speed = 94 * 5 / 18 m/s. Step 4: Calculate: 94 * 5 / 18 = 470 / 18 m/s which simplifies to approximately 26.11 m/s. Step 5: Time taken for slower train to pass the man = 9 seconds. Step 6: Distance covered relative to the man (equal to length of slower train) = relative speed * time. Step 7: Length of slower train = (470 / 18) * 9 = 470 / 2 = 235 m. Verification / Alternative check: We can verify by simplifying carefully. Since (470 / 18) * 9 equals 470 * 9 / 18, we can cancel 9 and 18 to get 470 / 2, which is 235 m. The units are metres, and this length is realistic for a train. With a relative speed of roughly 26.11 m/s, in 9 seconds the slower train would indeed cover about 235 m, confirming the result. Why Other Options Are Wrong: 338.4 m: This would require a longer time or higher relative speed than given. 470 m and 940 m: These are multiples of the relative speed factor but would correspond to 18 or 36 seconds, not 9 seconds, for the given relative speed. Common Pitfalls: Learners sometimes subtract speeds instead of adding them in opposite direction problems. Another typical error is to confuse which train length is involved. In this situation, only the slower train is passing the man, so we use its length, not the combined length of both trains. Incorrect unit conversion from km/h to m/s can also lead to wrong answers, so it is essential to handle the factor 5/18 accurately. Final Answer: The length of the slower train is 235 m.

Question 14

A train 110 m long is running at a speed of 60 km/h. In what time (in seconds) will it pass a man who is running at 6 km/h in the opposite direction to the train?

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Introduction / Context: This is a standard question on relative speed where a train passes a man running in the opposite direction. It tests the understanding that when two bodies move towards each other, their relative speed is the sum of their individual speeds, and that the distance to be covered during crossing is the train length only. Given Data / Assumptions: Train length = 110 m. Speed of train = 60 km/h. Speed of man = 6 km/h. They move in opposite directions along the same line. Speeds are constant and the track is straight. Concept / Approach: When two objects move towards each other, their relative speed is the sum of their speeds. To find how long the train takes to pass the man completely, we calculate this relative speed in metres per second, then divide the train length by the relative speed. This gives the crossing time in seconds. Step-by-Step Solution: Step 1: Relative speed in km/h = 60 + 6 = 66 km/h. Step 2: Convert 66 km/h to m/s using 1 km/h = 5/18 m/s. Step 3: Relative speed = 66 * 5 / 18 = 330 / 18 m/s, which simplifies to 55 / 3 m/s. Step 4: Distance to be covered relative to the man = length of train = 110 m. Step 5: Use time = distance / speed, so time = 110 / (55 / 3) seconds. Step 6: Simplify: time = 110 * 3 / 55 = 330 / 55 = 6 seconds. Verification / Alternative check: We can check by quick mental math. Relative speed 55 / 3 is about 18.33 m/s. In 6 seconds, distance = 18.33 * 6 ≈ 110 m, which matches the train length. This confirms that 6 seconds is the correct crossing time for the train to pass the man completely. Why Other Options Are Wrong: 5 sec: At this time the train would only cover about 91.67 m, which is less than its length. 7 sec: This would give over 128 m, more than the required 110 m, which does not match the crossing condition. 10 sec: This is too long and would involve the train covering much more distance than its length relative to the man. Common Pitfalls: Common mistakes include subtracting the man speed from the train speed even though they move in opposite directions, or using only the man speed by accident. Another typical error is forgetting to convert km/h to m/s, which leads to time values with wrong units. Remember that conversion and the idea that crossing a point object involves only train length are crucial to solving these problems correctly. Final Answer: The train will pass the man completely in 6 sec.

Question 15

A train is moving at a speed of 90 km/h. How many seconds will it take to cover a distance of 2275 m?

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Introduction / Context: This speed, distance, and time question asks how long a train moving at a constant speed takes to cover a fixed distance. Problems of this type are very common in aptitude tests and require careful unit conversion and straightforward formula application. Given Data / Assumptions: Speed of train = 90 km/h. Distance to be covered = 2275 m. The train moves at a constant speed in a straight line. Required answer is in seconds. Concept / Approach: The key relationship is time = distance / speed. To keep units consistent, we convert the speed from km/h to m/s so that the distance in metres divided by speed in metres per second gives time in seconds directly. Then we perform a simple division to get the final result. Step-by-Step Solution: Step 1: Convert speed from km/h to m/s using 1 km/h = 5/18 m/s. Step 2: Speed in m/s = 90 * 5 / 18 = 25 m/s. Step 3: Distance to be covered = 2275 m. Step 4: Use time = distance / speed, so time = 2275 / 25 seconds. Step 5: Compute 2275 / 25 = 91 seconds. Verification / Alternative check: We can verify by multiplying back. At 25 m/s, in 91 seconds the train covers 25 * 91 = 2275 m, exactly matching the given distance. The numbers are clean and the units are consistent, which confirms that our time calculation is correct. Why Other Options Are Wrong: 96 seconds: This implies a covered distance of 25 * 96 = 2400 m, which is greater than 2275 m. 86 seconds: This would give 25 * 86 = 2150 m, less than the required distance. 93 seconds: At this time, distance would be 25 * 93 = 2325 m, again not equal to 2275 m. Common Pitfalls: Mistakes often occur when converting from km/h to m/s, especially reversing the conversion factor. Another error is rounding too early, which can give slightly off results. Here, the division 2275 by 25 is exact and should be computed carefully to avoid arithmetic mistakes. Final Answer: The train will take 91 seconds to cover 2275 m.

Question 16

A train 100 m long is running at a speed of 120 km/h. How many seconds will it take to pass a person standing near the track?

Accepted Answer

Introduction / Context: This question focuses on the basic concept of a train passing a stationary observer. It is a direct application of time = distance / speed, where the relevant distance is only the length of the train, since the person is treated as a point on the ground. Given Data / Assumptions: Length of train = 100 m. Speed of train = 120 km/h. The person is standing still near the track. The train moves at constant speed along a straight track. Concept / Approach: When a train passes a stationary person, the distance it must cover to pass completely is equal to the length of the train. To find time, we convert the train speed from km/h to m/s and then divide train length by this speed. This yields the crossing time in seconds. Step-by-Step Solution: Step 1: Convert train speed from km/h to m/s using 1 km/h = 5/18 m/s. Step 2: Speed in m/s = 120 * 5 / 18 = 600 / 18 = 100 / 3 m/s. Step 3: Distance to be covered relative to the person = length of train = 100 m. Step 4: Use time = distance / speed, so time = 100 / (100 / 3) seconds. Step 5: Simplify: time = 100 * 3 / 100 = 3 seconds. Verification / Alternative check: Check by mental calculation. A speed of 100 / 3 m/s is approximately 33.33 m/s. Over 3 seconds, the train covers about 100 m, which exactly matches its length. This confirms that the person will see the entire train pass in 3 seconds from the first to the last coach. Why Other Options Are Wrong: 1 second: At this time, the train covers only about 33.33 m, far less than its length. 5 seconds: The train would cover about 166.67 m, more than its actual length. 7 seconds: This would give a distance of more than 230 m, which is clearly incorrect for a 100 m train. Common Pitfalls: A common error is forgetting to convert km/h to m/s correctly before computing time. Some learners also mistakenly add extra distance such as imaginary platform length even though the question only involves a stationary person. Remember that in person or pole crossing problems, only the train length is relevant for the distance calculation. Final Answer: The train will take 3 seconds to pass the person completely.

Question 17

A train that is 200 m long is running at a uniform speed of 54 km/hr. How many seconds will it take for the entire train to completely cross a bridge that is 175 m long, from the moment the engine reaches the bridge until the last coach leaves it?

Accepted Answer

Introduction / Context: This is a standard trains and relative motion question that focuses on the relationship between distance, speed, and time. The key idea is that when a train crosses a bridge or a platform, the distance it effectively covers is the sum of its own length and the length of the bridge. You then combine this distance with the speed (converted into consistent units) to find the time taken. Given Data / Assumptions: - Length of the train = 200 m. - Length of the bridge = 175 m. - Speed of the train = 54 km/hr (uniform speed). - The train must completely cross the bridge, which means the whole 200 m must clear the bridge length. - Motion is along a straight track with no acceleration or deceleration. Concept / Approach: The fundamental formula used in this problem is time = distance / speed. When a train crosses a bridge, the distance travelled from the instant the engine reaches the bridge until the last coach leaves it equals the sum of the train length and bridge length. Since the speed is given in km/hr and the lengths are in meters, we must convert the speed into meters per second before applying the formula. This ensures all units are consistent and avoids calculation mistakes. Step-by-Step Solution: Step 1: Total distance to be covered while crossing the bridge = length of train + length of bridge = 200 m + 175 m = 375 m.Step 2: Convert the train's speed from km/hr to m/s using the standard factor 5 / 18.Step 3: Speed in m/s = 54 * (5 / 18) = (54 / 18) * 5 = 3 * 5 = 15 m/s.Step 4: Use the time formula: time = distance / speed = 375 / 15 seconds.Step 5: Compute 375 / 15 = 25 seconds.Step 6: Therefore, the train takes exactly 25 seconds to completely cross the bridge. Verification / Alternative check: A quick reasonableness check: at 15 m/s, the train covers 150 m in 10 seconds, 300 m in 20 seconds, and 375 m in 25 seconds. This matches the calculated answer perfectly. Also, since both the train and bridge lengths are mid-range values and the speed is moderate, an answer around a few tens of seconds is realistic, which further supports 25 seconds as a sensible result. Why Other Options Are Wrong: 20 seconds would correspond to a distance of 20 * 15 = 300 m, which is less than the 375 m required. 12.5 seconds would only allow the train to cover about 187.5 m. 18 seconds corresponds to 270 m, and 15 seconds corresponds to 225 m. None of these distances is enough to cover both the 200 m train and the 175 m bridge together. Common Pitfalls: Learners often forget to add the bridge length to the train length and mistakenly use only 200 m in the distance. Another frequent mistake is neglecting to convert 54 km/hr into m/s, which leads to inconsistent units and incorrect answers. Some also round the conversion unnecessarily, but using the exact factor 5 / 18 keeps the calculation clean and accurate. Final Answer: The train will take 25 seconds to completely cross the 175 m long bridge.

Question 18

To travel a distance of 432 km, an Express train takes 1 hour more than the Duronto train. However, if the speed of the Express train is increased by 50%, it then takes 2 hours less than the Duronto for the same journey. What is the speed in km/hr o…

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Introduction / Context: This problem tests your understanding of speed, distance, and time relationships, combined with algebraic reasoning. Two trains, an Express and the Duronto, cover the same fixed distance, but their travel times change when the speed of one of them is altered. You must translate these time relations into equations and solve for the Duronto's speed. Given Data / Assumptions: - Distance between the two stations = 432 km. - Duronto train speed = v km/hr (to be found). - Express train speed = u km/hr (unknown intermediate). - Express takes 1 hour more than Duronto for 432 km. - When the speed of Express is increased by 50%, it then takes 2 hours less than Duronto for the same 432 km. - Both trains travel at constant speeds without extra stoppage times. Concept / Approach: For any journey, time = distance / speed. Let the time taken by Duronto be T_D and by Express be T_E. We know that T_E = T_D + 1 hour initially. When the Express speed becomes 1.5u, its new time T_E' becomes T_D - 2 hours. By expressing T_D, T_E and T_E' in terms of the distance and speeds, we can form equations in T_D and solve them without explicitly computing u, which simplifies the algebra. Step-by-Step Solution: Step 1: Let Duronto's time be T_D hours. Then T_D = 432 / v.Step 2: The Express takes 1 hour more, so its time T_E = T_D + 1 = 432 / u.Step 3: When the Express speed is increased by 50%, the new speed is 1.5u and the new time is T_E' = 432 / (1.5u) = T_D - 2.Step 4: From Step 2, u = 432 / (T_D + 1).Step 5: Substitute into T_E': 432 / (1.5u) = 432 / (1.5 * 432 / (T_D + 1)) = 432 * (T_D + 1) / (1.5 * 432) = (2/3) * (T_D + 1).Step 6: Set this equal to T_D - 2: (2/3) * (T_D + 1) = T_D - 2.Step 7: Multiply both sides by 3: 2(T_D + 1) = 3T_D - 6.Step 8: Simplify: 2T_D + 2 = 3T_D - 6, which gives T_D = 8 hours.Step 9: Duronto's speed v = distance / time = 432 / 8 = 54 km/hr. Verification / Alternative check: Check with actual times. Duronto: 432 / 54 = 8 hours. Express original time: 8 + 1 = 9 hours, so its speed is 432 / 9 = 48 km/hr. If Express speed increases by 50%, new speed = 1.5 * 48 = 72 km/hr. New travel time for Express = 432 / 72 = 6 hours. Duronto still takes 8 hours, so Express now takes 2 hours less, exactly matching the condition. Everything is consistent. Why Other Options Are Wrong: 60 km/hr would give Duronto time 7.2 hours, which does not satisfy the 1 hour more and 2 hours less conditions for the Express. 48 km/hr would wrongly assign the Duronto the original Express speed. 72 km/hr is the increased Express speed, not Duronto's. 64 km/hr similarly fails to satisfy the time relations when you compute the corresponding Express speeds. Common Pitfalls: Students often confuse which train is faster initially or mix up statements like "1 hour more" versus "2 hours less". Others attempt to build equations directly in terms of speeds u and v, which can be messy. Introducing Duronto's time T_D as a single variable simplifies the problem significantly and avoids unnecessary algebraic complications. Final Answer: The speed of the Duronto train is 54 km/hr.

Question 19

To travel a distance of 660 km, an Express train takes 10 hours more than the Rajdhani train. However, if the speed of the Express train is doubled, it then takes 7 hours less than the Rajdhani for the same journey. What is the speed of the Rajdhani…

Accepted Answer

Introduction / Context: This is another algebraic speed–time problem where two trains cover the same distance but with different speeds and time differences. The Express and the Rajdhani trains are compared under two scenarios, and you must deduce the speed of the Rajdhani using the relationships given. Given Data / Assumptions: - Distance between the two stations = 660 km. - Rajdhani speed = v km/hr (to be found). - Express speed = u km/hr (unknown intermediate value). - Initially, the Express takes 10 hours more than the Rajdhani: T_E = T_R + 10. - When the Express speed is doubled, it takes 7 hours less than the Rajdhani: T_E' = T_R - 7. - Both trains travel at constant speeds with no extra stoppages. Concept / Approach: We again use time = distance / speed. Let T_R be the time taken by Rajdhani. Then the Express time is T_R + 10. When the Express speed doubles, the travel time becomes half of its original time, but the question directly states the new time relative to T_R, which we can use. Express everything in terms of T_R and solve a simple linear equation for T_R first, then use it to get the Rajdhani speed. Step-by-Step Solution: Step 1: Let Rajdhani's time be T_R hours, so T_R = 660 / v.Step 2: Express's original time T_E = T_R + 10 = 660 / u.Step 3: When the Express speed is doubled (2u), its new time T_E' = 660 / (2u) = T_R - 7.Step 4: From Step 2, u = 660 / (T_R + 10).Step 5: Substitute u into T_E': 660 / (2u) = 660 / (2 * 660 / (T_R + 10)) = 660 * (T_R + 10) / (2 * 660) = (T_R + 10) / 2.Step 6: Set (T_R + 10) / 2 = T_R - 7 as given.Step 7: Multiply both sides by 2: T_R + 10 = 2T_R - 14.Step 8: Rearrange: 10 + 14 = 2T_R - T_R, so T_R = 24 hours.Step 9: Rajdhani speed v = distance / time = 660 / 24 = 27.5 km/hr. Verification / Alternative check: Check using actual times. Rajdhani: 660 / 27.5 = 24 hours as found. Original Express time: 24 + 10 = 34 hours, so original Express speed u = 660 / 34 ≈ 19.41 km/hr. When speed is doubled, new speed = 2u ≈ 38.82 km/hr and new time = 660 / (2u) = 17 hours. Rajdhani time is 24 hours, so the faster Express now takes exactly 7 hours less than the Rajdhani (24 - 7 = 17), matching the problem statement. Why Other Options Are Wrong: 38.8 km/hr and 50.1 km/hr are inconsistent with the 10 hour more and 7 hour less conditions when you recompute times. 16.2 km/hr would make Rajdhani unreasonably slow and break the given time differences. 33 km/hr also does not yield integer or consistent time gaps of 10 hours and 7 hours when substituted back. Common Pitfalls: Some learners mistakenly double the Express speed and assume the time difference is halved, which is not what the question says. Others attempt to solve directly for u and v simultaneously, which can be more complicated. Introducing T_R first and writing everything in terms of that single variable is a neat and reliable strategy. Final Answer: The speed of the Rajdhani train is 27.5 km/hr.

Question 20

The distance between places U and V is 1008 km. An express train leaves place U at 9:00 a.m., runs at a constant speed of 126 km/hr, and also stops on the way for a total of 20 minutes. At what time in the afternoon (p.m.) will the train reach place…

Accepted Answer

Introduction / Context: This question combines uniform speed motion with a fixed stoppage time. The express train travels a known distance at a constant speed and also halts for a specific duration. The task is to compute the overall journey time including stops and then convert this into an actual clock time of arrival. Given Data / Assumptions: - Distance between U and V = 1008 km. - Speed of the express train while moving = 126 km/hr. - Total stoppage time during the journey = 20 minutes. - Departure time from U = 9:00 a.m. - Train speed is constant whenever it is moving, and stoppage time is simply added to the running time. Concept / Approach: The main relationship is time = distance / speed for the running part of the journey. Once we compute the running time in hours, we add the additional stoppage time converted into hours. Finally, we add the total journey time to the 9:00 a.m. departure time to find the arrival time at V. Careful conversion of minutes to hours and correct handling of clock time are the key steps. Step-by-Step Solution: Step 1: Compute the pure running time (without stops) using time = distance / speed.Step 2: Running time = 1008 / 126 hours.Step 3: Since 126 * 8 = 1008, the running time is exactly 8 hours.Step 4: Convert the stoppage time of 20 minutes into hours: 20 minutes = 20 / 60 = 1/3 hour.Step 5: Total journey time = running time + stoppage time = 8 + 1/3 hours = 8 hours and 20 minutes.Step 6: Add this total journey time to the departure time of 9:00 a.m. Adding 8 hours gives 5:00 p.m., and adding 20 minutes gives 5:20 p.m. Verification / Alternative check: We can check reasonableness. A train at 126 km/hr covers roughly 120–130 km each hour. For a 1008 km journey, 1008 / 126 = 8 hours makes sense (about 8 * 125 = 1000 km). Adding a small 20-minute stop on top naturally leads to an arrival time slightly after 5:00 p.m. There are no other pauses or speed changes mentioned, so 5:20 p.m. is fully consistent. Why Other Options Are Wrong: 3:50 p.m. and 4:20 p.m. are much earlier than the minimum 8 hours required from 9:00 a.m. even without any stops. 6:50 p.m. would correspond to more than 9 hours and 30 minutes of total travel, which is too long for this distance and speed. 4:50 p.m. would correspond to a shorter travel time than 8 hours, again impossible at the given speed. Common Pitfalls: Some learners forget to add the 20-minute stoppage, using only the running time and ending at 5:00 p.m. Others incorrectly convert 20 minutes into hours or accidentally subtract instead of add the stoppage time. Another common mistake is to mis-handle the a.m. to p.m. transition when adding hours to 9:00 a.m. Final Answer: The express train will reach place V at 5:20 p.m.

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