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
3371
In a race of 800 meters, A can beat B by 40 meters. In a race of 500 meters, B can beat C by 5 meters. In a race of 200 meters, by what distance will A beat C?
Answer:
11.9 m
Ratio A:B = 800:760 = 20:19. Ratio B:C = 500:495 = 100:99. Combined ratio A:B:C = (20*100):(19*100):(19*99) = 2000:1900:1881. When A runs 2000 m, C runs 1881 m. When A runs 200 m, C runs 188.1 m. A beats C by 200 - 188.1 = 11.9 meters.
3372
A, B, and C run along a circular track of length 3 km with speeds of 10 km/h, 20 km/h, and 30 km/h respectively in the same direction. When will they meet for the first time?
Answer:
0.3 hours
Time for first meeting of all three is LCM of time taken for any two pairs to meet. T(A,B) = 3 / (20-10) = 3/10 hours. T(B,C) = 3 / (30-20) = 3/10 hours. T(A,C) = 3 / (30-10) = 3/20 hours. LCM of (3/10, 3/10, 3/20) = 3/10 hours = 0.3 hours.
3373
Two men start together to walk on a circular track of 400 meters with speeds of 10 m/s and 15 m/s respectively. If they move in opposite directions, when will they meet for the first time?
Answer:
16 s
When moving in opposite directions on a circular track, the relative speed is the sum of their individual speeds. Relative speed = 10 + 15 = 25 m/s. Time to meet = Distance / Relative Speed = 400 / 25 = 16 seconds.
3374
In a 400 m race, A gives B a start of 5 seconds and beats him by 15 m. In another race of 400 m, A beats B by 7 1/7 seconds. Their respective speeds are:
Answer:
8 m/s, 7 m/s
Let A's speed be x and B's be y. A beats B by 50/7 seconds means time taken by B - time taken by A = 50/7, so 400/y - 400/x = 50/7. In the first case, A beats B by 15 m after giving a 5s start. So B runs for (400/x + 5) seconds and covers 385 m. Thus, (400/x + 5)y = 385. Solving these simultaneously yields A's speed x = 8 m/s and B's speed y = 7 m/s.
3375
In a game of billiards, A can give B 15 points in 60 and A can give C 20 points in 60. How many points can B give C in a game of 90?
Answer:
10 points
When A scores 60, B scores 45 (60-15) and C scores 40 (60-20). The ratio of B's score to C's score is 45:40 or 9:8. In a game of 90, when B scores 90, C scores (8/9) * 90 = 80 points. Therefore, B can give C 90 - 80 = 10 points.
3376
A can run 22.5 m while B runs 25 m. In a kilometer race, B beats A by:
Answer:
100 m
The ratio of the distances covered by A and B is 22.5 : 25, which simplifies to 9 : 10. In a 1000 m race, when B covers 1000 m, A will cover (9/10) * 1000 = 900 m. Therefore, B beats A by 1000 - 900 = 100 m.
3377
In a race of 200 m, B can give a start of 10 m to A, and C can give a start of 20 m to B. Find the start that C can give to A in the same race.
Answer:
29 m
When B runs 200 m, A runs 190 m. When C runs 200 m, B runs 180 m. Ratio C:B = 200:180 = 10:9. Ratio B:A = 200:190 = 20:19. Combined ratio C:B:A = 200:180:171. When C runs 200 m, A runs 171 m. Therefore, C can give A a start of 200 - 171 = 29 m.
3378
In a 500 m race, the ratio of the speeds of two contestants A and B is 3:4. A has a start of 140 m. Then, A wins by:
Answer:
20 m
A needs to cover 500 - 140 = 360 m to finish. While A covers 3 m, B covers 4 m. When A covers 360 m, B covers (4/3) * 360 = 480 m. Since the total race is 500 m, B is still 500 - 480 = 20 m away from the finish line when A finishes. Thus, A wins by 20 m.
3379
A, B, and C run on a circular track of 800 m with speeds of 10 m/s, 20 m/s, and 30 m/s respectively. If they start from the same point and at the same time in the same direction, when will they meet for the first time at the starting point?
Answer:
80 s
Time taken by A to complete one round = 800/10 = 80 s. Time for B = 800/20 = 40 s. Time for C = 800/30 = 80/3 s. They meet at the starting point at the LCM of these times. LCM(80, 40, 80/3) = LCM(80, 40, 80) / HCF(1, 1, 3) = 80/1 = 80 seconds.
3380
In a 200 m race, A beats B by 31 m and C by 18 m. In a race of 350 m, by how many meters will C beat B?
Answer:
25 m
When A covers 200 m, B covers 200 - 31 = 169 m, and C covers 200 - 18 = 182 m. The ratio of distances covered by C and B is 182:169. When C runs 350 m, B runs (169/182) * 350 = 325 m. Therefore, C beats B by 350 - 325 = 25 m.