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
3381
A runs 1.75 times as fast as B. If A gives B a start of 84 m, how far must the winning post be so that A and B reach it at the same time?
Answer:
196 m
The ratio of speeds of A and B is 1.75 : 1, which is 7 : 4. This means in the same time, when A covers 7x meters, B covers 4x meters. A gains 3x meters over B. Here, the gain required is the start given, which is 84 m. So, 3x = 84, meaning x = 28. The total distance A runs is 7x = 7 * 28 = 196 m.
3382
In a game of 100 points, A can give B 20 points and C 28 points. Then, B can give C how many points in a game of 100?
Answer:
10 points
When A scores 100 points, B scores 80 points and C scores 72 points. This means when B scores 80, C scores 72. To find how many points C scores when B scores 100, we calculate: (72/80) * 100 = 90 points. Thus, in a game of 100, B can give C 100 - 90 = 10 points.
3383
In a 100 m race, A runs at 8 km/hr. If A gives B a start of 4 m and still beats him by 15 seconds, what is the speed of B?
Answer:
1.6 m/s
A's speed is 8 km/hr = 8 * (5/18) = 20/9 m/s. Time taken by A to cover 100 m is 100 / (20/9) = 45 seconds. A beats B by 15 seconds, so B takes 45 + 15 = 60 seconds to finish his race. Since A gave B a 4 m start, B runs only 96 m. B's speed = 96 m / 60 s = 1.6 m/s.
3384
A can run 1 km in 3 min 10 sec and B can cover the same distance in 3 min 20 sec. By what distance can A beat B?
Answer:
50 m
A's time = 190 seconds and B's time = 200 seconds. This means A beats B by 10 seconds. B covers 1000 m in 200 seconds, so B's speed is 1000/200 = 5 m/s. In the 10 seconds that B is behind, B would cover 5 * 10 = 50 m. Therefore, A beats B by 50 m.
3385
In a 1000 m race, A beats B by 100 m and B beats C by 100 m. By how many meters does A beat C in the same race?
Answer:
190 m
When A covers 1000 m, B covers 900 m. The ratio of their speeds is A:B = 1000:900 = 10:9. Similarly, when B covers 1000 m, C covers 900 m, so B:C = 10:9. The combined ratio A:B:C = 100:90:81. Thus, when A covers 1000 m (100*10), C covers 810 m (81*10). A beats C by 1000 - 810 = 190 m.
3386
In a 100 m race, A covers the distance in 36 seconds and B in 45 seconds. In this race, A beats B by what distance?
Answer:
20 m
A finishes the race in 36 seconds. In these 36 seconds, B is still running. B takes 45 seconds to run 100 m, so B's speed is 100/45 = 20/9 m/s. In 36 seconds, the distance covered by B is (20/9) * 36 = 80 m. Therefore, A beats B by 100 - 80 = 20 m.
3387
In a 1000 m race, A runs at 72 km/hr. A gives B a start of 100 m and beats him by 10 seconds. Find B's speed.
Answer:
15 m/s
Step 1: A's speed = 72 * 5/18 = 20 m/s. Time taken by A = 1000 / 20 = 50 seconds. Step 2: B's time = 50 + 10 = 60 seconds. B runs 1000 - 100 = 900 m. Step 3: B's speed = 900 / 60 = 15 m/s.
3388
In a 500 m race, A runs at 36 km/hr. A gives B a start of 50 m and beats him by 10 seconds. Find B's speed.
Answer:
7.5 m/s
Step 1: A's speed = 36 * 5/18 = 10 m/s. Time taken by A = 500 / 10 = 50 seconds. Step 2: B's time = 50 + 10 = 60 seconds. B runs 500 - 50 = 450 m. Step 3: B's speed = 450 / 60 = 7.5 m/s.
3389
In a 200 m race, A runs at 18 km/hr. A gives B a start of 10 m and beats him by 10 seconds. Find B's speed.
Answer:
3.8 m/s
Step 1: A's speed = 18 * 5/18 = 5 m/s. Time taken by A = 200 / 5 = 40 seconds. Step 2: B's time = 40 + 10 = 50 seconds. B runs 200 - 10 = 190 m. Step 3: B's speed = 190 / 50 = 3.8 m/s.
3390
In a 100 m race, A runs at 8 km/hr. If A gives B a start of 4 m and still beats him by 15 seconds, what is B's speed in m/s?
Answer:
1.6 m/s
Step 1: A's speed = 8 * 5/18 = 20/9 m/s. Time taken by A = 100 / (20/9) = 45 seconds. Step 2: B's time = 45 + 15 = 60 seconds. B runs 100 - 4 = 96 m. Step 3: B's speed = 96 / 60 = 1.6 m/s.