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
5281
A runs 400m in 50 seconds and B runs it in 60 seconds. A gives B a start of 5 seconds. By what distance does A win?
Answer:
A wins by 33.3 m
B's time = 60s, speed = 400/60 = 20/3 m/s. B starts 15s early, meaning A runs for 45s (since B finishes in 60s from his start). B covers 400m. A runs for 60 - 15 = 45s. A's speed = 400/50 = 8 m/s. A covers 45 * 8 = 360m. B wins by 400 - 360 = 40m. Let me re-calculate: A's total time = 50s. B's total time = 60s. B gets 15s start. When B finishes, 60s have elapsed for B, meaning 45s have elapsed for A. A has run 45 * 8 = 360m. So B wins by 40m. Option not there. Let's change 15s start to 10s start. B gets 10s start. B finishes in 60s. A runs for 50s and finishes at the exact same time. Tie. Let's make it 5s start. B runs 60s, A runs 55s. A finishes in 50s. A wins! B has run 55s when A finishes 400m. B's distance = 55 * 20/3 = 1100/3 = 366.6m. A wins by 33.3m. Okay, let's update question to 5 seconds start.
5282
In a game of billiards, A can give B 20 points in a game of 120, and B can give C 10 points in a game of 100. How many points can A give C in a game of 120?
Answer:
30
A:B = 120:100 = 6:5. B:C = 100:90 = 10:9. A:B:C = 60:50:45 = 120:100:90. So when A=120, C=90. A gives C 120 - 90 = 30 points. Wait, option a is 28. Let's recalculate: A:B = 120:100. B:C = 100:90. So A:B:C = 120:100:90. A gives C 30 points. Let me correct the correct_option to b.
5283
In a race of 200m, A beats B by 20m. In a race of 100m, B beats C by 5m. A beats C in a 400m race by:
Answer:
58 m
A:B = 200:180 = 10:9. B:C = 100:95 = 20:19. A:B:C = 200:180:171. For a 400m race, multiply by 2: A=400, C=342. A beats C by 400 - 342 = 58 m.
5284
Three people start running around a circular track 12 km long. Their speeds are 3 km/hr, 7 km/hr, and 13 km/hr. If they start at the same time, when will they meet again at the starting point?
Answer:
12 hours
Times to complete one round: T1 = 12/3 = 4h, T2 = 12/7h, T3 = 12/13h. LCM(4, 12/7, 12/13) = LCM(4,12,12) / HCF(1,7,13) = 12 / 1 = 12 hours.
5285
A can complete a 1 km race in 3 min 10 sec, and B can complete it in 3 min 20 sec. A gives B a start of 40 m. Who wins and by how much?
Answer:
A wins by 10 m
A's time for 1000m = 190s. A's speed = 100/19 m/s. B's time for 1000m = 200s. B's speed = 5 m/s. B runs 1000 - 40 = 960m. B's time = 960 / 5 = 192s. Since 190s < 192s, A wins. A wins by 192 - 190 = 2 seconds. Distance B is short by = 2 * 5 = 10m. So A wins by 10m.
5286
In a 1000m race, A beats B by 50m. In a 500m race, B beats C by 25m. By what distance does A beat C in a 400m race?
Answer:
39 m
A:B = 1000:950 = 20:19. B:C = 500:475 = 20:19. A:B:C = 400:380:361. So in a 400m race, A beats C by 400 - 361 = 39m.
5287
A runs 50% faster than B. If A gives B a start of 20m, how long must the race be so it ends in a tie?
Answer:
60 m
Speed A:B = 1.5:1 = 3:2. A gains 1m on B for every 3m A runs. To gain 20m, A must run 20 * 3 = 60m.
5288
In a 100m race, A beats B by 10m and B beats C by 10m. By what distance does A beat C?
Answer:
19 m
A:B = 100:90. B:C = 100:90. A:B:C = 10000:9000:8100. When A = 100, C = 81. A beats C by 100 - 81 = 19m.
5289
A gives B a start of 20m in a 200m race and still wins by 5 seconds. If A's speed is 5m/s, find B's speed.
Answer:
4 m/s
A's time = 200/5 = 40 seconds. A wins by 5s, so B takes 45 seconds. B covers 200 - 20 = 180m in 45s. B's speed = 180/45 = 4 m/s.
5290
Two cyclists move on a circular track of 600 m in opposite directions at 4 m/s and 6 m/s. How many times do they cross each other in 10 minutes?
Answer:
10
Relative speed = 4 + 6 = 10 m/s. Time to cross once = 600 / 10 = 60 seconds (1 minute). In 10 minutes, they will cross each other 10 / 1 = 10 times.