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
221
A car travels from A to B at 40 km/hr and returns from B to A at 60 km/hr. What is the average speed for the round trip?
Answer:
48 km/hr
When equal distances are covered at speeds S1 and S2, the average speed is given by (2 * S1 * S2) / (S1 + S2). Average speed = (2 * 40 * 60) / (40 + 60) = 4800 / 100 = 48 km/hr.
222
Walking at 5/6 of its usual speed, a train is 10 minutes late. Find its usual time to cover the journey.
Answer:
50 minutes
When speed becomes a/b of usual speed, the new time is b/a of usual time. Here, new time = 6/5 of usual time. The delay is (6/5)T - T = (1/5)T. Given (1/5)T = 10 minutes, the usual time T = 10 * 5 = 50 minutes.
223
If a man walks at 3/4 of his usual speed, he reaches his office 20 minutes late. What is his usual time to reach the office?
Answer:
60 minutes
Let his usual speed be S and usual time be T. Distance = S * T. New speed = (3/4)S, New time = T + 20. So, S * T = (3/4)S * (T + 20). Canceling S, we get T = (3/4)T + 15. Therefore, (1/4)T = 15, leading to T = 60 minutes.
224
A truck covers a distance in 8 hours. If its speed is increased by 10 km/hr, the same distance is covered in 6 hours. What is the original speed of the truck?
Answer:
30 km/hr
Let the original speed be S km/hr. Since distance is constant, S * 8 = (S + 10) * 6. Solving the equation: 8S = 6S + 60, which gives 2S = 60, so S = 30 km/hr. The original speed is 30 km/hr.
225
Three persons are walking from place A to place B. Their speeds are in the ratio 4:3:5. The ratio of the time taken by them to reach B will be:
Answer:
15:20:12
Time is inversely proportional to speed when the distance is constant. Let the speeds be 4x, 3x, and 5x. The ratio of time taken = (1/4) : (1/3) : (1/5). To simplify, multiply by the LCM of 4, 3, and 5, which is 60. The time ratio is 15 : 20 : 12.
226
The ratio of the speeds of two trains is 3:4. If the first train covers 300 km in 5 hours, what is the speed of the second train?
Answer:
80 km/hr
Speed of the first train = 300 km / 5 hrs = 60 km/hr. Since the ratio of speeds is 3:4, let the speeds be 3x and 4x. So, 3x = 60, which means x = 20. The speed of the second train is 4x = 4 * 20 = 80 km/hr.
227
A bus moving at a speed of 45 km/hr covers a certain distance in 1 hour 20 minutes. Find the distance.
Answer:
60 km
Convert time to hours: 1 hour 20 minutes = 1 + 20/60 = 1 + 1/3 = 4/3 hours. Distance = Speed * Time = 45 * (4/3) = 15 * 4 = 60 km. The bus covers 60 km in the given time.
228
A car travels at a speed of 80 km/hr. What is the distance it travels in 36 seconds?
Answer:
800 m
First, convert the speed from km/hr to m/s to match the time unit. Speed = 80 * (5/18) = 400/18 = 200/9 m/s. Distance = Speed * Time = (200/9) * 36 = 200 * 4 = 800 meters.
229
If an airplane covers 1440 km in 2 hours and 15 minutes, what is its speed?
Answer:
640 km/hr
Convert the time into a proper fraction of hours. 2 hours 15 minutes = 2 + 15/60 = 2 + 1/4 = 9/4 hours. Speed = Distance / Time = 1440 / (9/4) = 1440 * 4 / 9 = 160 * 4 = 640 km/hr.
230
A man crosses a 600-meter long street in 5 minutes. What is his speed in km per hour?
Answer:
7.2 km/hr
First, find the speed in m/s. Distance = 600 m, Time = 5 minutes = 5 * 60 = 300 seconds. Speed = 600 / 300 = 2 m/s. To convert m/s to km/hr, multiply by 18/5. Speed = 2 * (18/5) = 36 / 5 = 7.2 km/hr.