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
3281
Three people A, B, C run around a circular track of 400m at speeds of 2 m/s, 4 m/s, and 5 m/s respectively in the same direction. When will they all meet for the first time?
Answer:
400 s
Relative speeds wrt A: B - A = 2 m/s. C - A = 3 m/s. Time to meet A & B = 400/2 = 200s. Time to meet A & C = 400/3 s. LCM(200, 400/3) = 400 / 1 = 400 seconds.
3282
In a 100m race, A beats B by 10m and C by 20m. By what distance will B beat C in a 100m race?
Answer:
11.11 m
A:B = 100:90. A:C = 100:80. B:C = 90:80 = 9:8. When B runs 100m, C runs 100 * (8/9) = 88.88m. B beats C by 100 - 88.88 = 11.11m.
3283
A runs 3/2 times as fast as B. If A gives B a start of 40 m, how far is the winning post if the race is a dead heat?
Answer:
120 m
Speed A:B = 3:2. A gains 1m on B for every 3m he runs. To gain 40m, A must run 3 * 40 = 120 m.
3284
If A can run 1 km in 4 mins 20 s and B in 4 mins 40 s. A gives B a start of 50 m. Who wins and by how much distance?
Answer:
A wins by 21.4 m
A takes 260s, speed = 1000/260 = 50/13 m/s. B takes 280s, speed = 1000/280 = 25/7 m/s. B runs 950m. B's time = 950 / (25/7) = 266s. A finishes in 260s, so A wins. In the remaining 6s, B runs 6 * (25/7) = 150/7 ≈ 21.4 m. A wins by 21.4 m.
3285
A gives B a start of 20m in a 100m race and still wins by 2s. If B's speed is 4 m/s, A's speed is:
Answer:
5.5 m/s
B runs 80m. B's time = 80/4 = 20s. A wins by 2s, so A's time = 18s. A's speed = 100/18 = 50/9 ≈ 5.55 m/s. Closest is 5.5 m/s.
3286
In a game of 150 points, A gives B 30 points and C 45 points. How many points can B give C in a game of 120 points?
Answer:
15
A=150, B=120, C=105. Ratio B:C = 120:105. In a game of 120, B scores 120, C scores 105. B gives C 120 - 105 = 15 points.
3287
A beats B by 15s in a 300m race. If A's speed is 6 m/s, find B's speed.
Answer:
4.61 m/s
A's time = 300/6 = 50s. B's time = 50 + 15 = 65s. B's speed = 300/65 = 60/13 ≈ 4.61 m/s.
3288
In a 100m race, A beats B by 20m. To make the race a tie, A decides to start 20m behind the starting line. What happens?
Answer:
A wins
A:B speed ratio = 100:80 = 5:4. A runs 120m, taking time proportional to 120/5 = 24. B runs 100m, taking time proportional to 100/4 = 25. Since 24 < 25, A still wins.
3289
Two athletes run on a circular track of 400m in opposite directions at 5 m/s and 3 m/s. When do they meet for the second time?
Answer:
100 s
Relative speed = 5 + 3 = 8 m/s. Time for first meeting = 400 / 8 = 50s. Time for second meeting = 2 * 50 = 100s.
3290
In a 200m race, A beats B by 10m. If A's speed is 5 m/s, what is B's speed?
Answer:
4.75 m/s
A's time = 200/5 = 40s. B runs 200 - 10 = 190m in 40s. B's speed = 190/40 = 4.75 m/s.