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
5461
A tank is filled by two pipes in 17 min and 22 min respectively, and drained by a third pipe in 33 min. How long to fill the tank if all operate together?
Answer:
13.52
Step-by-step solution: 1. Filling rates: 1/17 + 1/22. 2. Draining rate: 1/33. 3. Net rate = 1/17 + 1/22 - 1/33 = 0.0740 tank/min. 4. Time = 1 / net rate = 13.52 minutes.
5462
A tank is filled by two pipes in 16 min and 21 min respectively, and drained by a third pipe in 31 min. How long to fill the tank if all operate together?
Answer:
12.84
Step-by-step solution: 1. Filling rates: 1/16 + 1/21. 2. Draining rate: 1/31. 3. Net rate = 1/16 + 1/21 - 1/31 = 0.0779 tank/min. 4. Time = 1 / net rate = 12.84 minutes.
5463
A tank is filled by two pipes in 19 min and 26 min respectively, and drained by a third pipe in 32 min. How long to fill the tank if all operate together?
Answer:
16.71
Step-by-step solution: 1. Filling rates: 1/19 + 1/26. 2. Draining rate: 1/32. 3. Net rate = 1/19 + 1/26 - 1/32 = 0.0598 tank/min. 4. Time = 1 / net rate = 16.71 minutes.
5464
A tank is filled by two pipes in 18 min and 22 min respectively, and drained by a third pipe in 30 min. How long to fill the tank if all operate together?
Answer:
14.78
Step-by-step solution: 1. Filling rates: 1/18 + 1/22. 2. Draining rate: 1/30. 3. Net rate = 1/18 + 1/22 - 1/30 = 0.0677 tank/min. 4. Time = 1 / net rate = 14.78 minutes.
5465
In a race of 600 m, A runs at 11 m/s and B at 10 m/s. What head start should A give B to finish together?
Answer:
54.55
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 600 m while B must cover 654.55 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 54.55 m.
5466
In a race of 550 m, A runs at 10 m/s and B at 9 m/s. What head start should A give B to finish together?
Answer:
55.0
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 550 m while B must cover 605.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 55.0 m.
5467
In a race of 900 m, A runs at 11 m/s and B at 10 m/s. What head start should A give B to finish together?
Answer:
81.82
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 900 m while B must cover 981.8199999999999 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 81.82 m.
5468
In a race of 600 m, A runs at 10 m/s and B at 9 m/s. What head start should A give B to finish together?
Answer:
60.0
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 600 m while B must cover 660.0 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 60.0 m.
5469
In a race of 400 m, A runs at 11 m/s and B at 10 m/s. What head start should A give B to finish together?
Answer:
36.36
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 400 m while B must cover 436.36 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 36.36 m.
5470
In a race of 1200 m, A runs at 9 m/s and B at 8 m/s. What head start should A give B to finish together?
Answer:
133.33
Step-by-step solution: 1. For a dead heat, both runners must take equal time. 2. Use time = distance / speed for each runner. 3. A covers 1200 m while B must cover 1333.33 m at the slower speed. 4. Head start = distance * (1 - speed_B/speed_A) = 133.33 m.