Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
191
A thief steals a car at 1:30 PM and drives it at 40 km/hr. The theft is discovered at 2:00 PM, and the owner sets off in another car at 50 km/hr. At what time will he overtake the thief?
Answer:
4:00 PM
From 1:30 PM to 2:00 PM (0.5 hours), the thief travels 40 * 0.5 = 20 km. The relative speed of the owner = 50 - 40 = 10 km/hr. Time required to close the 20 km gap = 20 / 10 = 2 hours. Therefore, he overtakes the thief at 2:00 PM + 2 hours = 4:00 PM.
192
Two trains 200 m and 150 m long are running on parallel rails in the same direction at speeds of 40 km/hr and 45 km/hr respectively. Time taken by the faster train to cross the slower train will be:
Answer:
252 seconds
Total distance = 200 + 150 = 350 m. Relative speed in the same direction = 45 - 40 = 5 km/hr. Convert relative speed to m/s: 5 * (5/18) = 25/18 m/s. Time = Distance / Relative Speed = 350 / (25/18) = (350 * 18) / 25 = 14 * 18 = 252 seconds.
193
A train overtakes two persons walking along a railway track in the same direction as the train. The first walks at 4.5 km/hr, the second at 5.4 km/hr. The train passes them in 8.4 and 8.5 seconds respectively. Find the speed of the train.
Answer:
81 km/hr
Let train speed be S km/hr and length be L km. Converting time to hours: 8.4s = 8.4/3600 hr. For first person: L = (S - 4.5) * (8.4/3600). For second person: L = (S - 5.4) * (8.5/3600). Equating L: (S - 4.5) * 8.4 = (S - 5.4) * 8.5 => 8.4S - 37.8 = 8.5S - 45.9 => 0.1S = 8.1 => S = 81 km/hr.
194
Two trains of equal length, running in opposite directions, pass a pole in 18 seconds and 12 seconds. The trains will cross each other in:
Answer:
14.4 seconds
Let the length of each train be L. Speed of first train = L/18. Speed of second train = L/12. Since they move in opposite directions, relative speed = L/18 + L/12 = (2L + 3L)/36 = 5L/36. Time to cross each other = Total distance / Relative speed = 2L / (5L/36) = 72L / 5L = 14.4 seconds.
195
A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. What is the speed of the train?
Answer:
50 km/hr
Relative speed of train to man = Distance / Time = 125 / 10 = 12.5 m/s. Converting to km/hr: 12.5 * (18/5) = 45 km/hr. Let the speed of the train be S. Since they are moving in the same direction, Relative Speed = S - 5. So, S - 5 = 45 => S = 50 km/hr.
196
A 300 m long train moving at 90 km/hr crosses another train moving in the same direction at 54 km/hr in 1 minute. What is the length of the second train?
Answer:
300 meters
Relative speed = 90 - 54 = 36 km/hr = 36 * (5/18) = 10 m/s. In 60 seconds (1 minute), the distance covered is 10 * 60 = 600 meters. Total distance = Length of train 1 + Length of train 2 => 600 = 300 + L2 => L2 = 300 meters.
197
Two trains traveling in the same direction at 40 km/hr and 22 km/hr completely pass each other in 1 minute. If the length of the first train is 125 meters, find the length of the second train.
Answer:
175 meters
Relative speed in same direction = 40 - 22 = 18 km/hr. Convert to m/s: 18 * (5/18) = 5 m/s. Distance covered in 60 seconds = 5 * 60 = 300 m. The total distance equals the sum of the lengths of both trains. Let the second train's length be L. 125 + L = 300 => L = 175 meters.
198
Two trains 140 m and 160 m long run at the speeds of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. What is the time they take to cross each other?
Answer:
10.8 seconds
Total distance = Sum of train lengths = 140 + 160 = 300 m. Since they travel in opposite directions, relative speed = Sum of speeds = 60 + 40 = 100 km/hr. Convert to m/s: 100 * (5/18) = 250/9 m/s. Time = Distance / Relative Speed = 300 / (250/9) = (300 * 9) / 250 = 2700 / 250 = 10.8 seconds.
199
Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively. They cross each other in 23 seconds. The ratio of their speeds is:
Answer:
3:2
Let the speeds of the two trains be S1 and S2 m/s. Length of first train = 27*S1. Length of second train = 17*S2. When crossing each other: Total distance = 27*S1 + 17*S2, Relative speed = S1 + S2. Time = (27*S1 + 17*S2) / (S1 + S2) = 23. Solving this: 27*S1 + 17*S2 = 23*S1 + 23*S2 => 4*S1 = 6*S2 => S1/S2 = 6/4 = 3/2. Ratio is 3:2.
200
A train crosses a platform 100 meters long in 60 seconds at a speed of 45 km/hr. Find the length of the train.
Answer:
650 meters
Speed = 45 * (5/18) = 12.5 m/s. Total distance covered in 60 seconds = 12.5 * 60 = 750 meters. Total distance = Length of train + Length of platform. 750 = Length of train + 100. Thus, length of train = 650 meters.