Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
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
121
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.
122
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.
123
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.
124
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.
125
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.
126
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.
127
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.
128
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.
129
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.
130
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.