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
2461
Pipes A and B fill a tank in 12 hours and 15 hours. Operating alternately starting with A, what is the total time?
Answer:
13.25 hours
Step 1: 2-hour cycle fills 1/12 + 1/15 = 9/60. Six cycles (12 hours) fill 54/60, leaving 6/60. Step 2: In the 13th hour, A fills 1/12 (or 5/60), leaving 1/60. Step 3: In the 14th hour, B's rate is 1/15 (or 4/60). Time for B = (1/60) / (4/60) = 1/4 hour. Total time = 13.25 hours.
2462
Pipe A fills a container in 10 hours and Pipe B in 20 hours. Opened on alternate hours starting with A, the filling time is:
Answer:
13 hours
Step 1: In a 2-hour cycle, they fill 1/10 + 1/20 = 3/20. Step 2: Six cycles (12 hours) fill 18/20. Remaining is 2/20 = 1/10. Step 3: A's turn comes next. A fills exactly 1/10 in 1 hour. Total time = 12 + 1 = 13 hours.
2463
Pipes A and B can fill a tank in 16 hours and 24 hours. Alternating every hour starting with A, how long does it take?
Answer:
19 hours
Step 1: A 2-hour cycle fills 1/16 + 1/24 = 5/48. Step 2: Nine cycles (18 hours) fill 45/48, leaving 3/48. Step 3: In the 19th hour, A (whose rate is 1/16 = 3/48) completely fills the remaining space in exactly 1 hour. Total time = 19 hours.
2464
Pipe A fills a pool in 15 hours and Pipe B in 20 hours. If opened on alternate hours starting with A, the total time is:
Answer:
17 hours
Step 1: Cycle of 2 hours fills 1/15 + 1/20 = 7/60. Step 2: Eight cycles (16 hours) will fill 8 * (7/60) = 56/60. The remaining part is 4/60 = 1/15. Step 3: In the 17th hour, it is A's turn. A fills exactly 1/15 in 1 hour. Total time = 17 hours.
2465
Pipes A and B fill a tank in 20 hours and 30 hours respectively. Operated on alternate hours starting with A, the tank fills in:
Answer:
24 hours
Step 1: A 2-hour cycle completes 1/20 + 1/30 = 5/60 = 1/12 of the tank. Step 2: Since 1/12 goes evenly into 1, exactly 12 full cycles are needed. Step 3: Total time = 12 cycles * 2 hours/cycle = 24 hours.
2466
Pipe A fills a cistern in 8 hours and Pipe B in 12 hours. If they are opened for alternate hours starting with A, how long will it take?
Answer:
9.5 hours
Step 1: In a 2-hour cycle, they fill 1/8 + 1/12 = 5/24. Four cycles (8 hours) will fill 20/24, leaving 4/24 (or 1/6) of the tank. Step 2: In the 9th hour, A fills 1/8 (or 3/24), leaving 1/24. Step 3: In the 10th hour, B takes (1/24) / (1/12) = 1/2 hour. Total time = 9.5 hours.
2467
Pipes A and B can fill a tank in 12 hours and 18 hours respectively. If they operate on alternate hours starting with A, what is the total time taken?
Answer:
14 1/3 hours
Step 1: In 2 hours, A and B fill 1/12 + 1/18 = 5/36. Step 2: 7 full cycles (14 hours) fill 35/36. Remaining is 1/36. Step 3: It's A's turn. A's rate is 1/12 per hour. Time for A = (1/36) / (1/12) = 1/3 hour. Total time = 14 + 1/3 hours.
2468
Pipe A fills a tank in 10 hours and Pipe B fills it in 15 hours. If they are opened on alternate hours starting with A, how long will it take to fill the tank?
Answer:
12 hours
Step 1: In a 2-hour cycle, A works for 1 hour and B for 1 hour. Total filled in 2 hours = 1/10 + 1/15 = 1/6 of the tank. Step 2: To fill the whole tank, we need 6 such cycles. Step 3: Total time = 6 cycles * 2 hours/cycle = 12 hours.
2469
Pipe A fills a reservoir in 20 hours and B in 60 hours. A is opened at 5 AM, B at 7 AM. At what time will the reservoir be filled?
Answer:
8:30 PM
Step 1: A runs alone for 2 hours, filling 2/20 = 1/10. Remaining is 9/10. Step 2: Combined rate = 1/20 + 1/60 = 4/60 = 1/15. Time to finish = (9/10) * 15 = 13.5 hours (13 hours 30 minutes). Step 3: Time from 7 AM + 13.5 hours = 8:30 PM.
2470
Pipes A and B fill a tank in 10 hours and 40 hours. A is opened at 4 PM, B at 5 PM. When will the tank be full?
Answer:
12:12 AM
Step 1: A works alone for 1 hour, filling 1/10. Remaining is 9/10. Step 2: Combined rate = 1/10 + 1/40 = 5/40 = 1/8. Time to finish = (9/10) * 8 = 7.2 hours (7 hours 12 minutes). Step 3: Time = 5 PM + 7 hours 12 minutes = 12:12 AM.