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
151
A person goes from A to B at a speed of 40 km/h and comes back from B to A at a speed of 60 km/h. What is his average speed?
Answer:
48 km/h
For equal distances, Average Speed = (2 * S1 * S2) / (S1 + S2) = (2 * 40 * 60) / (40 + 60) = 4800 / 100 = 48 km/h.
152
An athlete runs 200 meters race in 24 seconds. His speed is:
Answer:
30 km/hr
Speed = Distance / Time = 200 / 24 m/s. To convert to km/hr, multiply by 18/5. Speed = (200 / 24) * (18 / 5) = 3600 / 120 = 30 km/hr.
153
A train covers a distance of 10 km in 12 minutes. If its speed is decreased by 5 km/hr, the time taken to cover the same distance will be:
Answer:
13 minutes 20 seconds
Original speed = 10 km / (12/60) hr = 50 km/hr. New speed = 50 - 5 = 45 km/hr. Time taken = Distance / Speed = 10 / 45 hours = 2/9 hours. In minutes: (2/9) * 60 = 120/9 = 13.33 minutes = 13 minutes 20 seconds.
154
A plane covers a certain distance at a speed of 240 km/hr in 5 hours. To cover the same distance in 1 hour 40 minutes, it must travel at:
Answer:
720 km/hr
Distance = 240 * 5 = 1200 km. Time = 1 hour 40 minutes = 1 + 2/3 = 5/3 hours. New Speed = Distance / Time = 1200 / (5/3) = 1200 * 3 / 5 = 720 km/hr.
155
A man covers 2/3 of his journey at 40 km/h and the remaining at 20 km/h. His average speed for the whole journey is:
Answer:
30 km/h
Let total distance be 3D. Time 1 = 2D / 40. Time 2 = D / 20 = 2D / 40. Total time = 4D / 40 = D / 10. Average speed = Total Distance / Total Time = 3D / (D/10) = 30. Wait. Time 1 = 2D/40 = D/20. Time 2 = D/20. Total time = 2D/20 = D/10. Speed = 3D / (D/10) = 30. Let me check the math. If D=60, 2/3 is 40km, time = 1 hr. Remaining 1/3 is 20km, time = 1 hr. Total dist 60, total time 2 hrs. Avg speed 30. Option a is 30. Let me fix the option value.
156
A train passes a 50m long platform in 14 seconds and a man standing on the platform in 10 seconds. The speed of the train is:
Answer:
45 km/hr
The train covers its own length in 10 seconds. It covers (its own length + 50m) in 14 seconds. This means it covers 50m in (14 - 10) = 4 seconds. Speed = 50 / 4 = 12.5 m/s. In km/hr, Speed = 12.5 * (18/5) = 45 km/hr.
157
The speed of a car is 90 km/hr. What is the distance covered by it in 10 minutes?
Answer:
15 km
Speed = 90 km/hr. Time = 10 minutes = 10/60 = 1/6 hours. Distance = Speed * Time = 90 * (1/6) = 15 km.
158
If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:
Answer:
50 km
Let the actual time traveled be T hours. The distance is 10T. If he walks at 14 km/hr, distance is 14T. Difference = 14T - 10T = 4T = 20 km => T = 5 hours. Actual distance = 10 * 5 = 50 km.
159
How many minutes does a person take to cover a distance of 400m if he runs at a speed of 20 km/hr?
Answer:
1.2 minutes
Speed = 20 km/hr = 20 * (5/18) = 100/18 = 50/9 m/s. Time in seconds = Distance / Speed = 400 / (50/9) = 72 seconds. Time in minutes = 72 / 60 = 1.2 minutes.
160
A boat goes 15 km upstream and 22 km downstream in 5 hours. It goes 20 km upstream and 55/2 km downstream in 6.5 hours. What is the speed of the stream?
Answer:
3 km/hr
Let upstream speed be U and downstream be D. 15/U + 22/D = 5. Also, 20/U + 27.5/D = 6.5. Solving these linear equations gives U=5 and D=11. Speed of stream = (D - U)/2 = (11 - 5)/2 = 3 km/hr. Wait, let's recheck: Option b is 3. I will correct the option marking.