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
3321
Two men P and Q run a 4 km race on a circular track of 400 m. P runs at 5 m/s and Q runs at 4 m/s. How many times will P overtake Q?
Answer:
2
P finishes the race (4000m) in 4000/5 = 800s. Q finishes in 4000/4 = 1000s. Relative speed (same direction) = 5 - 4 = 1 m/s. Time for P to overtake Q once = Track Length / Relative Speed = 400 / 1 = 400s. In 800s, P overtakes Q exactly 800/400 = 2 times.
3322
A runs 5/3 times as fast as B. If A gives B a start of 80m, how far must the winning post be from the starting point so that they finish at the same time?
Answer:
200 m
Speed ratio A:B = 5:3. A gains 2m over B when A runs 5m. To gain the 80m start, A must run (5/2) * 80 = 200m.
3323
In a 1 km race, A, B, and C are three participants. A can give B a start of 50 m and C a start of 69 m. The start which B can allow C is:
Answer:
20 m
When A covers 1000m, B covers 950m and C covers 931m. Ratio B:C = 950:931. In a 1000m race, when B covers 1000m, C covers (931/950)*1000 = 980m. B can give C a start of 1000 - 980 = 20 m.
3324
A can give B 20 points in a game of 100, and B can give C 10 points in a game of 100. How many points can A give C in a game of 100?
Answer:
28 points
A/B = 100/80. B/C = 100/90. A/C = (100/80) * (100/90) = 10000/7200 = 100/72. Therefore, A can give C 100 - 72 = 28 points.
3325
In a 50m race, A beats B by 10m. In a 50m race, B beats C by 5m. By how many meters does A beat C in a 50m race?
Answer:
14 m
A:B = 50:40 = 5:4 = 50:40. B:C = 50:45 = 10:9 = 40:36. Thus A:B:C = 50:40:36. A beats C by 50 - 36 = 14 m.
3326
A gives B a start of 30m in a 150m race and A wins by 10m. What is the ratio of speeds of A to B?
Answer:
15:11
A runs 150m. B runs 150 - 30 - 10 = 110m in the same time. Ratio of speeds = Ratio of distances = 150:110 = 15:11.
3327
In a 400m race, A runs at 5 m/s. If A gives B a start of 20m and still beats him by 10 seconds, what is B's speed?
Answer:
4.2 m/s
A's time = 400/5 = 80s. B's time = 80 + 10 = 90s. B runs 400 - 20 = 380m in 90s. B's speed = 380/90 = 38/9 = 4.22 m/s. Closest is 4.2 m/s.
3328
In a 100m race, if A gives B a start of 20m, A wins by 5 seconds. If A gives B a start of 40m, the race ends in a dead heat. Find A's speed.
Answer:
6.66 m/s
In 2nd case, A giving 40m start implies B takes A's full time to run 60m. In 1st case, B gets 20m start and runs 80m. B takes 5s more than A to run 80m. This means B takes 5s to run the 20m difference (80m - 60m). So B's speed = 20/5 = 4 m/s. A's time equals B's time for 60m = 60/4 = 15s. A's speed = 100/15 = 20/3 = 6.66 m/s. Wait, let me adjust options. If A's time is 20s, B runs 60m in 20s => B=3m/s. Diff = 20m in 20/3 s... Let me provide 20/3m/s or change numbers. I will put option D as 6.66 m/s and select it.
3329
A can complete a round of a circular track in 2 mins, B in 3 mins and C in 4 mins. If they start from the same point simultaneously, when will they meet next at the starting point?
Answer:
12 mins
The time they meet at the starting point is the LCM of their individual times. LCM(2, 3, 4) = 12 minutes.
3330
Two athletes run a 2 km race. Athlete A beats B by 100 m or 20 seconds. What is the speed of athlete A?
Answer:
5.26 m/s
B runs 100 m in 20 seconds, so B's speed = 5 m/s. B's time for 2000m = 2000/5 = 400 seconds. A's time = 400 - 20 = 380 seconds. A's speed = 2000 / 380 = 100/19 = 5.26 m/s.