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
3251
A runs 1.5 times as fast as B. If A gives B a 25m start, how long must the race be to end in a tie?
Answer:
75 m
Speed A:B = 1.5:1 = 3:2. A gains 1m on B over 3m run. To gain 25m, A must run 25 * 3 = 75m.
3252
In a 1 km race, A beats B by 50m. In a 2 km race, A will beat B by:
Answer:
100 m
A:B ratio is 1000:950. In a 2000m race, A covers 2000m, B covers 1900m. A beats B by 100m.
3253
A circular track is 800m long. A, B, C start running at 2m/s, 4m/s, 8m/s in same direction. When will they meet at starting point?
Answer:
400 s
T_A = 800/2 = 400s. T_B = 800/4 = 200s. T_C = 800/8 = 100s. LCM(400, 200, 100) = 400s.
3254
A and B run a 100m race. A runs at 5 m/s. A gives B a 4m start and beats him by 4s. B's speed is?
Answer:
4 m/s
A's time = 100/5 = 20s. B's time = 20 + 4 = 24s. B runs 100 - 4 = 96m in 24s. B's speed = 96/24 = 4 m/s.
3255
A runs 3 times as fast as B. A gives B a start of 20m. The winning post is at 30m. Who wins and by what distance?
Answer:
Tie
A runs 30m. A takes time proportional to 30/3 = 10. B has 20m start, runs 10m. B takes time proportional to 10/1 = 10. Since times are equal, it's a tie.
3256
In a game of 60, A can give B 10 points and C 20 points. B can give C how many points in a game of 90?
Answer:
18
A=60, B=50, C=40. B:C = 50:40 = 5:4. In a game of 90, B=90, C=(4/5)*90=72. B gives C 90 - 72 = 18 points.
3257
A beats B by 20m in a 200m race. If A's speed is 8 m/s, find B's speed.
Answer:
7.2 m/s
A's time = 200/8 = 25s. B runs 180m in 25s. B's speed = 180/25 = 7.2 m/s.
3258
A can cover 1km in 4 min, B in 5 min. A gives B a start of 15 seconds. Who wins and by what distance?
Answer:
A wins by 150 m
A's time = 240s, B's time = 300s. B's speed = 1000/300 = 10/3 m/s. A finishes in 240s. B runs for 240 + 15 = 255s when A finishes. B covers 255 * 10/3 = 850m. A wins by 1000 - 850 = 150m. Let me recalculate. Options are small. B gets 15s start. B needs to run for 300s. A finishes in 240s. B has run 255s. Distance B left = 45s * 10/3 = 150m. I will update the options to include 150m.
3259
Two men start walking on a circular track 1 km long at speeds of 2 m/s and 3 m/s in the same direction. When will they meet for the first time?
Answer:
1000 s
Relative speed = 3 - 2 = 1 m/s. Distance = 1000m. Time = 1000 / 1 = 1000 seconds.
3260
A runs 5 times as fast as B. If A gives B a start of 80m, how far must the winning post be to end in a tie?
Answer:
100 m
A:B = 5:1. A gains 4m when running 5m. To gain 80m, A must run (5/4)*80 = 100m.