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
2471
Pipe A fills a tank in 12 hours, and B in 24 hours. A is opened at 9 AM, B at 11 AM. What time will the tank be completely filled?
Answer:
5:40 PM
Step 1: A runs alone for 2 hours (9 to 11 AM), filling 2/12 = 1/6. Remaining is 5/6. Step 2: Combined rate = 1/12 + 1/24 = 3/24 = 1/8. Time for remaining = (5/6) * 8 = 40/6 = 6.67 hours (6 hours 40 minutes). Step 3: Adding 6 hours 40 minutes to 11 AM gives 5:40 PM.
2472
Pipes A and B fill a cistern in 8 hours and 24 hours. A is opened at 2 PM, and B at 3 PM. When will the cistern be full?
Answer:
8:15 PM
Step 1: A runs alone for 1 hour, filling 1/8. Remaining is 7/8. Step 2: Combined rate = 1/8 + 1/24 = 4/24 = 1/6. Time for remaining = (7/8) * 6 = 42/8 = 5.25 hours (5 hours 15 minutes). Step 3: Time from 3 PM is 3 PM + 5 hours 15 minutes = 8:15 PM.
2473
Pipe A fills a tank in 5 hours, and Pipe B in 10 hours. A is opened at 1 PM, and B at 2 PM. At what time will it be fully filled?
Answer:
4:40 PM
Step 1: A runs for 1 hour (1 to 2 PM), filling 1/5. Remaining is 4/5. Step 2: Combined rate = 1/5 + 1/10 = 3/10. Time for remaining = (4/5) / (3/10) = 8/3 hours = 2 hours 40 minutes. Step 3: The tank fills at 2 PM + 2 hours 40 minutes = 4:40 PM.
2474
Pipes A and B fill a tank in 3 hours and 6 hours. A is opened at 10 AM, and B is opened at 11 AM. When is the tank full?
Answer:
12:20 PM
Step 1: A runs alone for 1 hour, filling 1/3 of the tank. The remaining portion is 2/3. Step 2: Combined rate = 1/3 + 1/6 = 1/2. Time to fill remaining = (2/3) / (1/2) = 4/3 hours = 1 hour 20 minutes. Step 3: From 11 AM, adding 1 hour 20 minutes gives 12:20 PM.
2475
Pipe A fills a drum in 4 hours, and Pipe B in 6 hours. Pipe A is opened at 8 AM, and Pipe B at 9 AM. When will the drum be filled?
Answer:
10:48 AM
Step 1: A runs alone for 1 hour, filling 1/4. Remaining is 3/4. Step 2: Combined rate = 1/4 + 1/6 = 5/12. Time for remaining = (3/4) / (5/12) = 9/5 hours = 1.8 hours = 1 hour 48 minutes. Step 3: The time is 9 AM + 1 hour 48 minutes = 10:48 AM.
2476
Pipes A and B fill a tank in 20 and 30 hours respectively. A is opened at 7 AM and B at 9 AM. At what time will the tank be completely filled?
Answer:
7:48 PM
Step 1: A runs alone for 2 hours (7 to 9 AM), filling 2/20 = 1/10 of the tank. Remaining part is 9/10. Step 2: Combined rate is 1/20 + 1/30 = 5/60 = 1/12 per hour. Time for remaining part = (9/10) * 12 = 10.8 hours (10 hours 48 minutes). Step 3: Adding to 9 AM, 9 AM + 10 hours 48 minutes = 7:48 PM.
2477
Pipe A can fill a cistern in 12 hours and B in 18 hours. A is opened at 10 AM, B at 11 AM. When will the cistern be completely filled?
Answer:
5:36 PM
Step 1: A runs alone for 1 hour (10 to 11 AM), filling 1/12. Remaining is 11/12. Step 2: Combined rate is 1/12 + 1/18 = 5/36. Time to fill remaining = (11/12) / (5/36) = 11/12 * 36/5 = 33/5 = 6.6 hours (6 hours 36 minutes). Step 3: The cistern will be filled at 11 AM + 6 hours 36 minutes = 5:36 PM.
2478
Pipe A fills a tank in 10 hours, and Pipe B in 15 hours. Pipe A is opened at 8 AM, and Pipe B is opened at 9 AM. At what time will the tank be fully filled?
Answer:
2:24 PM
Step 1: From 8 AM to 9 AM, only A operates. A fills 1/10 of the tank. The remaining part is 9/10. Step 2: From 9 AM, both operate. Combined rate = 1/10 + 1/15 = 1/6 per hour. Time for remaining 9/10 = (9/10) * 6 = 5.4 hours (5 hours 24 minutes). Step 3: Total time from 9 AM = 9 AM + 5 hours 24 minutes = 2:24 PM.
2479
A tank is filled by Pipe A in 8 hours. Pipe B empties it at a rate of 3 liters per minute. Both open, the tank fills in 12 hours. What is the capacity?
Answer:
4320 liters
Step 1: Find the time for B to empty the tank. 1/8 - 1/B = 1/12 => 1/B = 1/8 - 1/12 = 3/24 - 2/24 = 1/24. B takes 24 hours. Step 2: Convert 24 hours to minutes: 24 * 60 = 1440 minutes. Step 3: Capacity = 1440 minutes * 3 liters/minute = 4320 liters.
2480
Pipe A fills a tank in 20 hours. Pipe B empties the tank at 10 liters per hour. Working together, they fill the tank in 25 hours. What is the tank's capacity?
Answer:
1000 liters
Step 1: Let Pipe B empty the tank in B hours. 1/20 - 1/B = 1/25. Step 2: Calculate 1/B: 1/B = 1/20 - 1/25 = 5/100 - 4/100 = 1/100. B takes 100 hours to empty the tank. Step 3: Capacity = Time * Rate = 100 hours * 10 liters/hour = 1000 liters.