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
171
Pipes A, B, and C can fill a tank in 12, 18, and 36 hours. What is the total filling time when all operate simultaneously?
Answer:
6 hours
Step 1: Extract the hourly rates: 1/12, 1/18, and 1/36. Step 2: Add the rates using a common denominator: 3/36 + 2/36 + 1/36 = 6/36. Step 3: The fraction simplifies to 1/6, meaning the tank will be completely filled in 6 hours.
172
Three pipes fill a cistern in 30, 40, and 120 minutes respectively. Together, how many minutes will they take?
Answer:
15 minutes
Step 1: Convert the times to minute rates: 1/30, 1/40, and 1/120. Step 2: Find the total rate by summing the fractions: 4/120 + 3/120 + 1/120 = 8/120. Step 3: Simplify 8/120 to 1/15. The pipes will completely fill the cistern in 15 minutes.
173
Taps A, B, and C can fill a reservoir in 18, 24, and 72 hours respectively. How much time is taken if all taps are opened?
Answer:
9 hours
Step 1: The individual filling rates are 1/18, 1/24, and 1/72 per hour. Step 2: Add the rates together: 4/72 + 3/72 + 1/72 = 8/72. Step 3: Simplify the combined rate to 1/9. The total time taken to fill the reservoir is exactly 9 hours.
174
Three pipes fill a container in 10, 20, and 60 minutes respectively. If all are opened together, how many minutes will it take?
Answer:
6 minutes
Step 1: Determine the per-minute filling rates: 1/10, 1/20, and 1/60. Step 2: Sum these rates using 60 as the common denominator: 6/60 + 3/60 + 1/60 = 10/60. Step 3: Simplify 10/60 to 1/6. The reciprocal shows that the container fills in 6 minutes.
175
Pipes X, Y, and Z can fill a drum in 6, 8, and 24 hours. When opened simultaneously, how much time is needed to fill the drum?
Answer:
3 hours
Step 1: Write down the individual hourly work rates: 1/6, 1/8, and 1/24. Step 2: Add the rates: 4/24 + 3/24 + 1/24 = 8/24. Step 3: The sum simplifies to 1/3. Therefore, the pipes will completely fill the drum in 3 hours.
176
A tank is filled by three pipes in 8, 12, and 24 hours individually. What is the total time taken if all three are opened together?
Answer:
4 hours
Step 1: Identify the rate of each pipe per hour: 1/8, 1/12, and 1/24. Step 2: Add the fractions to find the combined rate: 3/24 + 2/24 + 1/24 = 6/24. Step 3: Simplify the fraction to 1/4. Since they fill 1/4 of the tank per hour together, it takes 4 hours.
177
Pipes A, B, and C can fill a pool in 15, 20, and 30 hours respectively. If all three are opened at once, how long does it take?
Answer:
6.67 hours
Step 1: The individual rates are 1/15, 1/20, and 1/30. Step 2: Sum the rates to get the combined rate: 4/60 + 3/60 + 2/60 = 9/60 = 3/20. Step 3: Time taken is the reciprocal, 20/3 hours. Converting this to a decimal gives exactly 6.66... hours, or 6.67 hours rounded.
178
Three taps can fill a tank in 20, 24, and 30 hours respectively. How many hours will it take to fill the tank if all are opened together?
Answer:
8 hours
Step 1: Calculate the per-hour rate for each tap: 1/20, 1/24, and 1/30. Step 2: Add these rates using a common denominator (120): 6/120 + 5/120 + 4/120 = 15/120. Step 3: Simplify the fraction to 1/8. This means the taps together fill 1/8 of the tank per hour, taking 8 hours to fill it entirely.
179
Pipes P, Q, and R fill a cistern in 12, 15, and 20 hours respectively. If all are opened simultaneously, find the time to fill the cistern.
Answer:
5 hours
Step 1: The individual filling rates per hour are 1/12, 1/15, and 1/20. Step 2: Determine the total rate by summing the individual rates: 1/12 + 1/15 + 1/20 = 5/60 + 4/60 + 3/60 = 12/60. Step 3: Reduce 12/60 to 1/5. The total time required to fill the cistern is 5 hours.
180
Three pipes A, B, and C can fill a tank in 10, 12, and 15 hours respectively. If all three are opened together, how long will it take to fill the tank?
Answer:
4 hours
Step 1: Find the hourly rate of each pipe: A = 1/10, B = 1/12, C = 1/15. Step 2: Add their rates together to find the combined hourly rate: 1/10 + 1/12 + 1/15 = 6/60 + 5/60 + 4/60 = 15/60. Step 3: Simplify the combined rate: 15/60 = 1/4. It will take 4 hours to fill the tank.