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
3331
On a circular track of 1200m, two cyclists start together from the same point in the same direction at 15 m/s and 25 m/s. When will they meet for the first time?
Answer:
120 s
Relative speed = 25 - 15 = 10 m/s. Time to meet = Distance / Relative Speed = 1200 / 10 = 120 seconds.
3332
A and B run a 1 km race. A gives B a start of 40m and beats him by 10s. If A runs at 8m/s, find the speed of B.
Answer:
7.1 m/s
A's time = 1000/8 = 125s. A beats B by 10s, so B takes 135s. B runs 1000 - 40 = 960m in 135s. B's speed = 960/135 = 64/9 = 7.11 m/s.
3333
In a race of 200m, A can beat B by 10m and C by 20m. In a race of 190m, B will beat C by:
Answer:
10 m
A:B = 200:190. A:C = 200:180. Thus B:C = 190:180. In a 190m race, when B runs 190m, C runs 180m. B beats C by 190 - 180 = 10 m.
3334
A 400m race is run by A and B. A beats B by 20m. B and C run the same race, B beats C by 40m. By what distance does A beat C?
Answer:
58 m
A:B = 400:380 = 20:19. B:C = 400:360 = 10:9. A:B:C = 200:190:171. A race of 400m means multiply by 2: A=400, C=342. A beats C by 400 - 342 = 58 m.
3335
A runs 2.5 times as fast as B. If A gives B a start of 30 m, how long should the race be so they finish together?
Answer:
50 m
Speed A:B = 2.5:1 = 5:2. A gains 3m over every 5m he runs. To gain 30m, A must run 5 * (30/3) = 50m. Let's recheck: A runs 50m, B runs 20m. A gives 30m start, 50-20=30m. So race length is 50m. Wait, 5*(30/3) = 50m. Option c is 60m. Let me correct the option to 50m.
3336
A, B and C play billiards. A can give B 10 points in 50 and C 20 points in 50. How many points can B give C in a game of 40?
Answer:
10 points
When A = 50, B = 40, C = 30. Ratio B:C = 40:30 = 4:3. In a game of 40, B = 40, C = 30. B gives C 40 - 30 = 10 points.
3337
In a 100m race, A covers the distance in 10s and B covers it in 12s. What distance can A give B to make the race a dead heat?
Answer:
16.66 m
B's speed = 100/12 = 25/3 m/s. A finishes in 10s, so B runs for 10s and covers 10 * 25/3 = 250/3 = 83.33 m. The start A must give B is 100 - 83.33 = 16.66 m.
3338
A beats B by 10 seconds in a 1000m race. If A's speed is 5 m/s, what is B's speed?
Answer:
4.76 m/s
A's time = 1000/5 = 200 s. B's time = 200 + 10 = 210 s. B's speed = 1000/210 = 100/21 = 4.76 m/s.
3339
In a 500 m race, the ratio of speeds of two participants is 3:4. If the slower participant has a start of 150 m, what is the outcome?
Answer:
Slower wins by 33.3 m
Slower (A) needs 350 m to finish. A:B speed ratio is 3:4. When A covers 350 m, B covers 350 * (4/3) = 466.67 m. Since the total distance is 500 m, B is short by 500 - 466.67 = 33.3 m. Slower wins by 33.3 m.
3340
If A can give B a start of 10m in a 100m race, and B can give C a start of 10m in a 100m race, how much start can A give C in a 100m race?
Answer:
19 m
A:B = 100:90. B:C = 100:90. A:B:C = 10000 : 9000 : 8100. For a 100m race (dividing by 100), A = 100, C = 81. A can give C a start of 100 - 81 = 19 m.