All Categories MCQs
Topic Notes: All Categories
General Description
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
3291
A and B start a 1 km race. A runs at 10 m/s. B runs at 8 m/s. What start in distance should A give B for a dead heat?
Answer:
200 m
A's time = 1000/10 = 100s. For a dead heat, B must also run for 100s. Distance B covers in 100s = 8 * 100 = 800m. A must give B a start of 1000 - 800 = 200m.
3292
In a game of 60 points, A scores 60 while B scores 45. In another game of 60, B scores 60 while C scores 40. In a game of 60, how many points can A give C?
Answer:
30
A:B = 60:45 = 4:3. B:C = 60:40 = 3:2. A:B:C = 4:3:2 = 60:45:30. A gives C 60 - 30 = 30 points.
3293
A runs 4 times as fast as B. If A gives B a start of 90m, how far must the winning post be from the start so they tie?
Answer:
120 m
A:B = 4:1. A gains 3m for every 4m he runs. To gain 90m, A must run (4/3) * 90 = 120m.
3294
A gives B a start of 30 seconds in a 1000m race and still wins by 20m. If A runs at 8 m/s, what is B's speed?
Answer:
6.3 m/s
A's time = 1000/8 = 125s. A wins by 20m, meaning B was at 980m when A finished. But B had a 30s start, so B ran for 125 + 30 = 155s to cover 980m. B's speed = 980/155 = 196/31 ≈ 6.32 m/s.
3295
A, B and C run on a circular track of 600m. A runs at 3 m/s, B at 4 m/s, and C at 5 m/s in the same direction. When will they meet for the first time?
Answer:
600 s
Relative speeds: Vb - Va = 1 m/s, Vc - Vb = 1 m/s. Time to meet A & B = 600/1 = 600s. Time to meet B & C = 600/1 = 600s. LCM(600, 600) = 600 seconds.
3296
In a 100 m race, A beats B by 20m and C by 28m. In a 50m race, B will beat C by:
Answer:
5 m
A:B = 100:80. A:C = 100:72. B:C = 80:72 = 10:9. In a 50m race, B runs 50m, C runs (9/10)*50 = 45m. B beats C by 5m.
3297
In a 1000 m race, A can beat B by 50 m or 10 seconds. What is the time taken by A to complete the race?
Answer:
190 s
B runs 50 m in 10 seconds, so B's speed is 5 m/s. B's time for 1000m = 1000/5 = 200s. A beats B by 10s, so A's time = 200 - 10 = 190 seconds.
3298
A runs 5/3 times as fast as B. If A gives B a start of 60 m, how far must the goal be so that both finish at the same time?
Answer:
150 m
Ratio of speeds A:B = 5:3. A gains 2m over B when A runs 5m. To gain 60m, A must run (5/2) * 60 = 150 m.
3299
In a game of 100 points, A can give B 20 points and B can give C 25 points. How many points can A give C?
Answer:
40
A:B = 100:80 = 5:4. B:C = 100:75 = 4:3. A:B:C = 5:4:3 = 100:80:60. A gives C 100 - 60 = 40 points.
3300
A gives B a start of 5 seconds in a 1000 m race. If A runs at 10 m/s and B runs at 8 m/s, who wins and by how many meters?
Answer:
A wins by 160 m
A finishes in 1000/10 = 100s. B runs for 100 + 5 = 105s when A finishes. Distance covered by B = 105 * 8 = 840 m. A wins by 1000 - 840 = 160 m.