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
181
A filling pipe takes 24 hours to fill a tank, while an emptying pipe takes 36 hours to empty it. When both are open, how long will it take to fill the tank?
Answer:
72 hours
Step 1: The rate of filling is 1/24 per hour. The rate of emptying is 1/36 per hour. Step 2: Calculate the combined net rate: 1/24 - 1/36 = 3/72 - 2/72 = 1/72. Step 3: The reciprocal of 1/72 represents the total time. Thus, it will take exactly 72 hours to fill the tank.
182
Pipe 1 can fill a tank in 10 hours. Pipe 2 can empty it in 20 hours. What is the time required to fill the tank if both are opened?
Answer:
20 hours
Step 1: Define the rates: Pipe 1 = +1/10, Pipe 2 = -1/20. Step 2: Calculate the net rate: 1/10 - 1/20 = 2/20 - 1/20 = 1/20. Step 3: The positive fraction indicates the tank is filling at a rate of 1/20 per hour. It will take 20 hours to fill.
183
A cistern has a filling pipe taking 4 hours and an emptying pipe taking 6 hours. If both are opened, how long to fill the empty cistern?
Answer:
12 hours
Step 1: Filling rate is 1/4. Emptying rate is 1/6. Step 2: Find the net hourly rate: 1/4 - 1/6 = 3/12 - 2/12 = 1/12. Step 3: Since 1/12 of the cistern fills every hour, the total time required to fill it is 12 hours.
184
Pipe A fills a pool in 6 hours. Pipe B can empty the full pool in 9 hours. If both run simultaneously, how many hours will it take to fill the pool?
Answer:
18 hours
Step 1: Pipe A's rate is 1/6 per hour. Pipe B's rate is -1/9 per hour. Step 2: Combine the rates: 1/6 - 1/9 = 3/18 - 2/18 = 1/18. Step 3: The overall net rate is 1/18 of the pool per hour. Therefore, it will take 18 hours to completely fill the pool.
185
A tap fills a cistern in 15 hours. Due to a leak at the bottom, it takes 25 hours to fill. In what time will the leak alone empty the full cistern?
Answer:
37.5 hours
Step 1: The normal filling rate is 1/15. The effective rate with the leak is 1/25. Let the leak's emptying rate be 1/x. Step 2: Form the equation: 1/15 - 1/x = 1/25. Step 3: Solve for 1/x: 1/x = 1/15 - 1/25 = 5/75 - 3/75 = 2/75. The time taken by the leak alone is 75/2 = 37.5 hours.
186
Pipe X fills a tank in 12 hours. Pipe Y empties the full tank in 18 hours. If both are opened, what is the total time taken to fill the tank?
Answer:
36 hours
Step 1: Identify rates. Filling rate is 1/12, and emptying rate is -1/18. Step 2: The net filling rate per hour is 1/12 - 1/18 = 3/36 - 2/36 = 1/36. Step 3: The reciprocal of the net rate gives the time. Thus, it will take 36 hours to completely fill the tank.
187
A pipe can fill a drum in 20 minutes, but a drain can empty the full drum in 30 minutes. If both are left open, how long will it take to fill the drum?
Answer:
60 minutes
Step 1: Convert the times to per-minute rates. Inlet rate = 1/20, Outlet rate = 1/30. Step 2: Find the net rate per minute: 1/20 - 1/30 = 3/60 - 2/60 = 1/60. Step 3: The net rate is 1/60 per minute. This means it will take exactly 60 minutes (or 1 hour) to fill the drum.
188
An inlet pipe fills a tank in 5 hours. An outlet pipe empties it in 10 hours. If both pipes are opened simultaneously, when will the tank be full?
Answer:
10 hours
Step 1: Determine the rates: Fill rate = 1/5 per hour, Empty rate = -1/10 per hour. Step 2: Calculate the effective filling rate: 1/5 - 1/10 = 2/10 - 1/10 = 1/10. Step 3: Since the effective rate is 1/10 of the tank per hour, the entire tank will be filled in 10 hours.
189
A cistern can be filled by an inlet pipe in 8 hours and emptied by an outlet pipe in 12 hours. If both are opened, find the time to fill the cistern.
Answer:
24 hours
Step 1: The inlet pipe fills 1/8 of the cistern per hour. The outlet pipe empties 1/12 of the cistern per hour. Step 2: The net hourly work is 1/8 - 1/12 = 3/24 - 2/24 = 1/24. Step 3: Because the net work is positive, the cistern is filling. It will take exactly 24 hours to become full.
190
Pipe A fills a tank in 10 hours, while Pipe B can empty the full tank in 15 hours. If both are opened together, how long will it take to fill the tank?
Answer:
30 hours
Step 1: Identify the nature of the pipes. A is an inlet (positive rate = 1/10) and B is an outlet (negative rate = -1/15). Step 2: Calculate the net filling rate: 1/10 - 1/15. The LCM is 30, so 3/30 - 2/30 = 1/30. Step 3: A net rate of +1/30 means the tank fills at a rate of 1/30th per hour. Total time required is 30 hours.