Sharpen your problem-solving skills with this CAT quantitative aptitude quiz focused on the core principles of time, speed, and distance. Tackle real-world scenarios and boost your preparation for competitive exams with medium-level questions designed for accuracy and understanding.
Two trains, Train A and Train B, are moving towards each other on parallel tracks at speeds of 60 km/h and 40 km/h respectively. If the length of each train is 120 meters, how long will it take for the trains to completely cross each other from the moment their front ends meet?
Explanation: When trains move in opposite directions, their relative speed adds up: 60 + 40 = 100 km/h. Converting to m/s: (100 × 1000)/3600 = 27.78 m/s. The total distance to be covered is 120 + 120 = 240 meters. Time = distance/speed = 240/27.78 ≈ 8.64 seconds. The options 10.8 and 12.96 seconds use incorrect speeds or neglect unit conversion, while 7.2 seconds underestimates the time due to calculation errors.
Rahul drives from City X to City Y at 60 km/h and returns at 40 km/h. What is his average speed for the entire journey?
Explanation: Average speed for a round trip when distances are equal is (2 × 60 × 40)/(60 + 40) = 4800/100 = 48 km/h. Choosing 50 km/h and 52 km/h ignores the harmonic mean formula, while 45 km/h misapplies direct means. The correct answer uses the right approach for two different speeds over equal distances.
A cyclist travels at a uniform speed of 15 km/h and covers a certain distance in 4 hours 30 minutes. What is the total distance covered?
Explanation: Time is 4.5 hours (since 30 minutes is 0.5 hours). Distance = speed × time = 15 × 4.5 = 67.5 km. The options 60 km and 52.5 km result from miscalculating time or speed, while 48 km reflects use of the wrong figures. 67.5 km correctly applies the distance formula.
Alice starts from Point A towards Point B at 5 km/h while Bob starts from Point B towards Point A at 7 km/h. If the distance between A and B is 48 km, after how many hours will they meet?
Explanation: When two objects move towards each other, add their speeds: 5 + 7 = 12 km/h. Time to meet = distance/relative speed = 48/12 = 4 hours. Choosing 3.5 or 5 hours comes from incorrect speed addition or subtraction, and 6 hours assumes only one is moving. 4 hours is accurate and uses the correct approach.
Priya normally takes 90 minutes to walk to school at a speed of 4 km/h. If she increases her speed to 6 km/h, how long will she take to cover the same distance to school?
Explanation: Distance = speed × time = 4 km/h × 1.5 h = 6 km. New time = distance/new speed = 6 km/6 km/h = 1 hour or 60 minutes. 45 minutes is too short, 75 and 54 minutes are based on incorrect use of speed-to-time ratios. 60 minutes is the right calculation.