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
3351
In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
Answer:
28 m
A:B = 100:75 = 4:3. B:C = 100:96 = 25:24. Combined ratio A:B:C = (4*25) : (3*25) : (3*24) = 100 : 75 : 72. So when A finishes 100m, C is at 72m. A beats C by 100 - 72 = 28 m.
3352
A, B and C run a 1000 m race. A beats B by 50 m and B beats C by 100 m. By how much does A beat C?
Answer:
145 m
Ratio A:B = 1000:950 = 20:19. Ratio B:C = 1000:900 = 10:9. A:B:C = 200:190:171. In a 1000 m race, multiply ratio by 5: A = 1000, C = 855. A beats C by 1000 - 855 = 145 m.
3353
A and B run a kilometer race. A wins by 60 seconds. A and C run the same race, A wins by 200 m. B and C run the same race, B wins by 30 seconds. What is the time taken by A to run 1 km?
Answer:
360 s
Let A's time be t. B's time = t + 60. C's time = B's time + 30 = t + 90. A beats C by 200m, meaning C covers 800m in t seconds. C's speed = 800/t. Also C's speed = 1000/(t+90). Equating them: 800/t = 1000/(t+90) => 4(t+90) = 5t => 4t + 360 = 5t => t = 360 seconds. Oh wait, my option says 240s. Let's recalculate: A beats B by 60s, B beats C by 30s. So A beats C by 90s. C takes t+90s for 1000m. C covers 800m in A's time t. So 800/t = 1000/(t+90). 4/t = 5/(t+90). 4t + 360 = 5t => t=360s. Option given doesn't match. I will update the options.
3354
In a 100 m race, A covers the distance in 25 seconds. B takes 30 seconds. A beats B by:
Answer:
16.66 m
B's speed = 100/30 = 10/3 m/s. In 25 seconds, B covers (10/3) * 25 = 250/3 m = 83.33 m. A beats B by 100 - 83.33 = 16.66 m.
3355
A runs twice as fast as B. If A gives B a start of 20 m, how long should the race course be so that both finish at the exact same time?
Answer:
40 m
A runs 2m for every 1m B runs, gaining 1m. To gain 20m, A must run 20 * 2 = 40m. The race course must be 40m long.
3356
A, B, and C run on a circular track. A completes a round in 12 mins, B in 15 mins, and C in 18 mins. If they start simultaneously, after how many minutes will they meet again at the starting point?
Answer:
180 mins
They will meet at the starting point at a time which is the LCM of their individual times. LCM(12, 15, 18) = 180. They will meet after 180 minutes.
3357
Two boys start running from the same point in opposite directions on a circular track of 600m. Their speeds are 3 m/s and 7 m/s. How many times will they cross each other before meeting at the starting point?
Answer:
10
Ratio of their speeds is 3:7. Since they run in opposite directions, the number of meeting points on the track is the sum of the terms of their speed ratio in simplest form. 3 + 7 = 10. They will cross each other 10 times.
3358
In a 300 m race, A beats B by 15 m or 5 seconds. What is A's speed?
Answer:
3.15 m/s
B runs 15 m in 5 seconds. B's speed = 15/5 = 3 m/s. B's total time for 300 m = 300/3 = 100 seconds. A's time = 100 - 5 = 95 seconds. A's speed = 300 / 95 = 60 / 19 ≈ 3.15 m/s.
3359
In a game of 80 points, A can give B 5 points and C 15 points. Then how many points can B give C in a game of 60?
Answer:
8 points
When A = 80, B = 75, C = 65. The ratio of B's score to C's score is 75:65 = 15:13. In a game of 60 points, when B scores 60, C scores (13/15) * 60 = 52 points. So, B can give C 60 - 52 = 8 points.
3360
A can run 45 meters while B runs 50 meters. In a 1 km race, B beats A by how many meters?
Answer:
100 m
The ratio of distances covered is A:B = 45:50 = 9:10. In a 1000 m race, when B covers 1000 m, A covers (9/10) * 1000 = 900 m. Therefore, B beats A by 1000 - 900 = 100 m.