Let the total distance be D. On the first attempt, Speed = S, Time = T. So, D = S * T. On the second attempt: For the first half of the distance (D/2), the speed is S * (1 + 0.10) = 1.1S. Time taken for the first half (t1) = (D/2) / (1.1S) = D / (2.2S). For the second half of the distance (D/2), the speed is S * (1 - 0.10) = 0.9S. Time taken for the second half (t2) = (D/2) / (0.9S) = D / (1.8S). Total time for the second attempt (T') = t1 + t2 = D / (2.2S) + D / (1.8S). Factor out D/S (which equals T from the first attempt): T' = (D/S) * (1/2.2 + 1/1.8) = T * (1/2.2 + 1/1.8). Convert the fractions: 1/2.2 = 10/22 = 5/11 and 1/1.8 = 10/18 = 5/9. Sum the fractions: 5/11 + 5/9 = (5*9 + 5*11) / (11*9) = (45 + 55) / 99 = 100/99. So, T' = T * (100/99). Since 100/99 is greater than 1, T' will be greater than T. Therefore, the cyclist will complete the route in more time on her second attempt. Why others are wrong: A — An equal percentage increase and decrease in speed, when applied over equal distances, does not result in a net reduction in time; the slower speed is applied for a longer duration. C — The arithmetic mean of speeds (which would imply the same time) is not appropriate here because the time spent at each speed is different, even though the distances are equal. D — The relationship can be determined through proportional reasoning without needing specific numerical values for distance or speed.

The cars are moving towards each other, so their speeds add up to form their relative speed. Relative speed = Speed of Car X + Speed of Car Y Relative speed = 60 km/h + 40 km/h = 100 km/h. The total distance to be covered for them to meet is the initial distance between them. Distance = 300 km. Time = Distance / Relative Speed. Time = 300 km / 100 km/h = 3 hours. Why others are wrong: A — Incorrect calculation; possibly from misinterpreting relative speed or a division error. C — Incorrect calculation; possibly from misinterpreting relative speed or a division error. D — This would be the time if only Car X were to cover the entire 300 km distance alone (300 km / 60 km/h = 5 hours), which is incorrect as Car Y is also moving.

Let C be the time taken to cycle one way from Town A to Town B (or B to A). Let W be the time taken to walk one way from Town A to Town B (or B to A). The distance for one way is constant. From the statement "If the person had cycled both ways, the journey would have taken 2 hours": 2C = 2 hours So, C = 1 hour (time to cycle one way). From the statement "a person cycles one way and walks back. This entire journey takes 4 hours and 30 minutes": C + W = 4 hours 30 minutes = 4.5 hours. Substitute the value of C into this equation: 1 hour + W = 4.5 hours W = 4.5 hours - 1 hour W = 3.5 hours (time to walk one way). The question asks for the time taken to walk both ways, which is 2W. 2W = 2 * 3.5 hours = 7 hours. Why others are wrong: A — This option might result from an arithmetic error or miscalculation of walking time. B — This option might be chosen if the walking time was incorrectly determined (e.g., 2.5 hours one way). D — This option might arise from a calculation error, such as misinterpreting the total time or individual leg times.

1. Calculate the time taken for the journey from City A to City B: Time = Distance / Speed = 300 km / 60 km/h = 5 hours. 2. Calculate the time taken for the return journey from City B to City A: Time = Distance / Speed = 300 km / 75 km/h = 4 hours. 3. Find the difference in time: 5 hours - 4 hours = 1 hour. Why others are wrong: A — Correct calculation. B — Incorrect calculation, possibly from miscalculation of one of the journey times. C — Incorrect calculation, possibly by adding instead of subtracting or a significant arithmetic error. D — Incorrect calculation, indicating a misunderstanding of the speed/time relationship or an arithmetic error.

1. Calculate the time taken for the first part of the journey: Time1 = Distance1 / Speed1 = 120 km / 60 km/h = 2 hours. 2. Calculate the time taken for the second part of the journey: Time2 = Distance2 / Speed2 = 150 km / 50 km/h = 3 hours. 3. Calculate the total distance covered: Total Distance = 120 km + 150 km = 270 km. 4. Calculate the total time taken: Total Time = Time1 + Time2 = 2 hours + 3 hours = 5 hours. 5. Calculate the average speed for the entire journey: Average Speed = Total Distance / Total Time = 270 km / 5 hours = 54 km/h. Why others are wrong: A — Incorrect calculation, likely from miscalculating total time or distance. C — This is the simple arithmetic mean of the two speeds (60+50)/2 = 55 km/h, which is incorrect for average speed when different times are spent at each speed. D — Incorrect calculation, likely from miscalculating total time or distance.