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
161
Pipes M and N fill a pool in 5 and 10 hours respectively. Pipe O empties the pool in 20 hours. If all are open, how long until the pool is full?
Answer:
4 hours
Step 1: Find individual hourly rates: M = +1/5, N = +1/10, O = -1/20. Step 2: Sum the rates to get the net rate: 4/20 + 2/20 - 1/20 = 5/20. Step 3: Simplify 5/20 to 1/4. A net rate of 1/4 means the pool will be completely full in 4 hours.
162
Two taps fill a cistern in 6 hours and 8 hours. A third tap empties it in 12 hours. Find the time taken to fill the empty cistern if all taps are open.
Answer:
4.8 hours
Step 1: Identify rates: +1/6, +1/8, and -1/12. Step 2: Calculate the net filling rate using a common denominator of 24: 4/24 + 3/24 - 2/24 = 5/24. Step 3: The total time is 24/5 hours. Converting this to a decimal yields 4.8 hours.
163
Pipe A fills a tank in 12 hours, Pipe B fills it in 24 hours, and Pipe C empties it in 8 hours. If all three are opened together on an empty tank, what will happen?
Answer:
Tank will never fill
Step 1: Determine the hourly rates: A = +1/12, B = +1/24, C = -1/8. Step 2: Calculate the net rate: 2/24 + 1/24 - 3/24 = 3/24 - 3/24 = 0. Step 3: Since the net rate is exactly 0, the volume of water entering equals the volume leaving. An empty tank will never accumulate water.
164
Inlets A and B fill a tank in 24 and 36 hours, while outlet C empties it in 72 hours. What is the total filling time when all are opened?
Answer:
18 hours
Step 1: The individual rates are +1/24, +1/36, and -1/72. Step 2: Calculate the net rate: 3/72 + 2/72 - 1/72 = 4/72. Step 3: Simplify 4/72 to 1/18. The tank will take 18 hours to completely fill.
165
Pipe A and B fill a tank in 10 and 15 minutes respectively. Pipe C empties it in 30 minutes. If all are open, how long to fill the tank?
Answer:
7.5 minutes
Step 1: Get the per-minute rates: 1/10, 1/15, and -1/30. Step 2: Add them together: 3/30 + 2/30 - 1/30 = 4/30. Step 3: Simplify the rate to 2/15. The total time required is 15/2 minutes, which equals 7.5 minutes.
166
Two taps can fill a tub in 8 and 12 hours, while a drain can empty it in 24 hours. How long does it take to fill the tub when all are open?
Answer:
6 hours
Step 1: Inlet rates are 1/8 and 1/12; the outlet rate is -1/24. Step 2: Add the rates to get the net rate: 1/8 + 1/12 - 1/24 = 3/24 + 2/24 - 1/24 = 4/24. Step 3: The sum simplifies to 1/6. Consequently, the tub will be filled in 6 hours.
167
Pipes P and Q fill a tank in 20 hours and 30 hours respectively. Pipe R can empty the full tank in 15 hours. If all three operate together, what will happen?
Answer:
Fills in 60 hours
Step 1: The rates for the filling pipes are 1/20 and 1/30. The emptying pipe's rate is -1/15. Step 2: Calculate the net rate: 1/20 + 1/30 - 1/15 = 3/60 + 2/60 - 4/60 = 1/60. Step 3: Because the net rate is positive (+1/60), the tank is filling, and it will take exactly 60 hours to become full.
168
Pipe A fills a tank in 12 hours, Pipe B fills it in 15 hours, and Pipe C empties it in 20 hours. What is the time to fill the tank if all are opened?
Answer:
10 hours
Step 1: The filling rates are 1/12 and 1/15, and the emptying rate is 1/20. Step 2: The net hourly rate is 1/12 + 1/15 - 1/20. With LCM 60: 5/60 + 4/60 - 3/60 = 6/60. Step 3: The fraction simplifies to 1/10. Therefore, the tank will be filled in 10 hours.
169
Two inlet pipes can fill a cistern in 15 hours and 20 hours respectively. A third pipe can empty it in 30 hours. How long will it take to fill the cistern with all three pipes open?
Answer:
12 hours
Step 1: Establish the individual rates: +1/15, +1/20, and -1/30. Step 2: Sum the rates to find the net effective filling rate: 4/60 + 3/60 - 2/60 = 5/60. Step 3: Simplify 5/60 to 1/12. This means the cistern will be fully filled in 12 hours.
170
Pipe A and Pipe B can fill a tank in 10 hours and 12 hours respectively, while Pipe C empties the full tank in 20 hours. If all three are opened, how long will it take to fill the tank?
Answer:
7.5 hours
Step 1: Inlet rates are 1/10 and 1/12. The outlet rate is -1/20. Step 2: The combined net rate is 1/10 + 1/12 - 1/20. Using a common denominator of 60: 6/60 + 5/60 - 3/60 = 8/60. Step 3: Simplify 8/60 to 2/15. The time required is 15/2 hours, which is exactly 7.5 hours.