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
121
A train 360m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140m long?
Answer:
40 sec
Total distance = 360 + 140 = 500m. Speed = 45 * 5/18 = 12.5 m/s. Time = 500 / 12.5 = 40 seconds.
122
A person travels a certain distance at 3 km/hr and reaches 15 minutes late. If he travels at 4 km/hr, he reaches 15 minutes early. The distance he has to travel is:
Answer:
6 km
Time difference = 15 + 15 = 30 minutes = 0.5 hours. Distance = (S1 * S2) / (S2 - S1) * Time Diff = (3 * 4) / 1 * 0.5 = 12 * 0.5 = 6 km.
123
A truck covers a distance of 550 km in 11 hours. What is the average speed of the truck?
Answer:
50 km/hr
Average Speed = Total Distance / Total Time = 550 / 11 = 50 km/hr.
124
Two cars travel the same distance at speeds of 60 km/h and 40 km/h respectively. If the slower car takes 2 hours longer than the faster car, what is the distance?
Answer:
240 km
Let distance be D. D/40 - D/60 = 2 => (3D - 2D)/120 = 2 => D/120 = 2 => D = 240 km.
125
A boy goes to school at a speed of 3 km/h and returns to the village at a speed of 2 km/h. If he takes 5 hours in all, what is the distance between the village and the school?
Answer:
6 km
Let distance be D. Total time = D/3 + D/2 = 5 => 5D/6 = 5 => D = 6 km.
126
A train M leaves Meerut at 5 AM and reaches Delhi at 9 AM. Another train N leaves Delhi at 7 AM and reaches Meerut at 10:30 AM. At what time do the two trains cross each other?
Answer:
7:56 AM
Train M takes 4 hours. Train N takes 3.5 hours. Let distance be 28 km (LCM of 4 and 3.5 is 28). Speed of M = 7 km/h. Speed of N = 8 km/h. M starts at 5 AM, N at 7 AM. By 7 AM, M covers 14 km. Distance left = 14 km. Relative speed = 15 km/h. Time to meet = 14/15 hours = 56 minutes. They cross at 7:56 AM.
127
A man covers 3/4 of his journey by bus at 45 km/hr and the remaining by walk at 15 km/hr. His average speed for the whole journey is:
Answer:
30 km/hr
Let total distance be 4D. Distance by bus = 3D, Distance by walk = D. Time by bus = 3D/45 = D/15. Time by walk = D/15. Total time = 2D/15. Average speed = 4D / (2D/15) = 60 / 2 = 30 km/hr.
128
Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. Find the time they take to cross each other.
Answer:
10.8 seconds
Relative speed = 60 + 40 = 100 km/hr = 100 * (5/18) = 250/9 m/s. Total distance = 140 + 160 = 300 m. Time = 300 / (250/9) = 2700 / 250 = 10.8 seconds.
129
A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Answer:
89 seconds
Speed of train = 240 / 24 = 10 m/s. Total distance to pass platform = 240 + 650 = 890 m. Time = 890 / 10 = 89 seconds.
130
If I walk at 5 km/hr, I miss a train by 7 minutes. However, if I walk at 6 km/hr, I reach the station 5 minutes before the departure. The distance to the station is:
Answer:
6 km
Time difference = 7 minutes late + 5 minutes early = 12 minutes = 12/60 = 1/5 hours. Distance = (5 * 6) / (6 - 5) * (1/5) = 30 * (1/5) = 6 km.