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
3341
In a 200 m race, X beats Y by 20 m and Z by 40 m. In a 100 m race, by how many meters will Y beat Z?
Answer:
11.11 m
When X = 200, Y = 180, Z = 160. Ratio Y:Z = 180:160 = 9:8. In a 100 m race, when Y = 100, Z = 100 * (8/9) = 88.88 m. Y beats Z by 100 - 88.88 = 11.11 m.
3342
A can cover 1 km in 4 minutes, B in 5 minutes, and C in 6 minutes. What start can A give C in a 1 km race to finish in a dead heat?
Answer:
333.33 m
A takes 240 s, C takes 360 s. C's speed = 1000/360 = 25/9 m/s. A beats C by 360 - 240 = 120 s. The distance C would cover in 120 s is 120 * (25/9) = 3000/9 = 333.33 m. So A must give C a start of 333.33 m.
3343
Two runners A and B run on a circular track of 500 m. A's speed is 4 m/s and B's speed is 6 m/s. If they run in opposite directions, when will they meet for the first time?
Answer:
50 s
Relative speed (opposite directions) = 4 + 6 = 10 m/s. Distance = 500 m. Time to meet = 500 / 10 = 50 seconds.
3344
A can complete a circular track in 15 seconds, B in 20 seconds. If they start from the same point simultaneously in the same direction, after how much time will they meet at the starting point?
Answer:
60 s
They will meet at the starting point at a time which is the LCM of their individual times. LCM of 15 and 20 is 60. They meet after 60 seconds.
3345
A runs 3 times as fast as B. If A gives B a start of 40 m, how far must the winning post be from the start so that both reach at the same time?
Answer:
60 m
A:B speed ratio = 3:1. A gains 2 m on B for every 3 m A runs. To gain 40 m, A must run (3/2) * 40 = 60 m. The goal must be 60 m away.
3346
In a 1000 m race, X beats Y by 150 m and Z by 200 m. By what distance does Y beat Z in a 850 m race?
Answer:
50 m
When X = 1000, Y = 850, Z = 800. The ratio Y:Z is 850:800. Therefore, in an 850 m race, when Y finishes 850 m, Z is at 800 m. Y beats Z by 850 - 800 = 50 m.
3347
In a 200 m race, A runs at 5 km/hr. A gives B a start of 10 m and still beats him by 10 seconds. Find the speed of B in m/s.
Answer:
1.23 m/s
A's speed = 5 * 5/18 = 25/18 m/s. A's time for 200 m = 200 / (25/18) = 144 s. B takes 144 + 10 = 154 s. B runs 200 - 10 = 190 m. B's speed = 190 / 154 = 95 / 77 ≈ 1.23 m/s.
3348
In a game of 100 points, A scores 100 points while B scores only 80 points. By how many points can A give B a start so that the game ends in a tie?
Answer:
20 points
Since A scores 100 when B scores 80, A outscores B by 20 points in a 100-point game. Thus, A can give B a 20-point start to make it a tie.
3349
In a 500 m race, A reaches the final post in 28 s and B reaches in 35 s. By how much distance does A beat B?
Answer:
100 m
A beats B by 35 - 28 = 7 seconds. B's speed = 500 / 35 = 100 / 7 m/s. In 7 seconds, B covers (100/7) * 7 = 100 m. Therefore, A beats B by 100 m.
3350
A can run 1 km in 4 minutes and B can run it in 4 min 10 sec. How many meters start can A give B in a 1 km race so that the race ends in a dead heat?
Answer:
40 m
A takes 240 seconds, B takes 250 seconds. A beats B by 10 seconds. B's speed = 1000/250 = 4 m/s. The distance B covers in 10 seconds is 4 * 10 = 40 m. A must give B a start of 40 m for a dead heat.