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
3311
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.
3312
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.
3313
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.
3314
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.
3315
In a race of 200 meters, A beats B by 20 meters or 5 seconds. What is the time taken by A to complete the race?
Answer:
45 s
B covers 20m in 5 seconds. B's speed = 20/5 = 4 m/s. B's total time = 200/4 = 50 seconds. A beats B by 5 seconds, so A's time = 50 - 5 = 45 seconds.
3316
A gives B a start of 5 seconds in a 1000m race. If A runs at 10m/s and B runs at 8m/s, by how much distance does A win?
Answer:
160 m
A finishes in 1000/10 = 100 seconds. B runs for 100 + 5 = 105 seconds when A finishes. B covers 105 * 8 = 840 m. A wins by 1000 - 840 = 160 m.
3317
A, B and C walk 1 km in 5 mins, 8 mins and 10 mins respectively. C starts walking from a point at a certain time, B starts from the same point 1 min later and A starts from the same point 2 mins later than C. Then A meets B and C at times:
Answer:
5/3 min, 2 min
Speeds: Va = 1/5 km/min, Vb = 1/8 km/min, Vc = 1/10 km/min. When A starts, C has walked for 2 mins (distance = 2/10 = 1/5 km). Relative speed A vs C = 1/5 - 1/10 = 1/10 km/min. A meets C in (1/5) / (1/10) = 2 mins. When A starts, B has walked for 1 min (distance = 1/8 km). Relative speed A vs B = 1/5 - 1/8 = 3/40. A meets B in (1/8) / (3/40) = 5/3 mins.
3318
In a game of 60 points, A can give B 15 points. In a game of 60 points, B can give C 20 points. How many points can A give C in a game of 60?
Answer:
30 points
A:B = 60:45 = 4:3. B:C = 60:40 = 3:2. A:B:C = 12:9:6 = 60:45:30. When A scores 60, C scores 30. A can give C 60 - 30 = 30 points.
3319
A covers a distance of 1 km in 4 minutes 54 seconds and B in 5 minutes. In a 1 km race, by what distance can A beat B?
Answer:
20 m
A takes 294s, B takes 300s. A beats B by 6s. B's speed = 1000/300 = 10/3 m/s. In 6 seconds, B runs 6 * 10/3 = 20m. A beats B by 20m.
3320
In a 100m race, A beats B by 10m and C by 13m. In a race of 180m, B will beat C by:
Answer:
6 m
A:B = 100:90. A:C = 100:87. So B:C = 90:87. In a 180m race, when B runs 180m (90*2), C runs 87*2 = 174m. B beats C by 180 - 174 = 6 m.