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
191
Pipe M fills a tank in 6 hours, while Pipe N fills the same tank in 8 hours. How long will it take for both to fill the tank together?
Answer:
3.42 hours
Step 1: Combine their hourly rates. Rate of M = 1/6, Rate of N = 1/8. Step 2: Total rate = 1/6 + 1/8 = 4/24 + 3/24 = 7/24. Step 3: The total time is 24/7 hours. Since 24 divided by 7 is approximately 3.428 hours, 3.42 hours is the correct choice.
192
A pipe can fill a water tank in 18 hours and a second pipe can fill it in 36 hours. If both pipes are opened, the tank will be filled in:
Answer:
12 hours
Step 1: The rate of the first pipe is 1/18, and the second pipe's rate is 1/36. Step 2: Add these rates to find the overall filling speed: 1/18 + 1/36 = 2/36 + 1/36 = 3/36. Step 3: Simplify 3/36 to 1/12. Therefore, both pipes working together will fill the tank in 12 hours.
193
Pipe P can fill a tub in 10 minutes, and Pipe Q can fill it in 40 minutes. Working together, what is the total time required?
Answer:
8 minutes
Step 1: Write down the per-minute filling rates for both pipes: P = 1/10 and Q = 1/40. Step 2: Find the combined rate by adding the two fractions together: 1/10 + 1/40 = 4/40 + 1/40 = 5/40 = 1/8. Step 3: The total time is the reciprocal of the combined rate, which equals 8 minutes.
194
Two pipes can fill a tank in 8 hours and 24 hours respectively. If they are opened simultaneously, what is the time taken to fill the tank?
Answer:
6 hours
Step 1: Establish the individual work rates. Pipe 1 fills at 1/8 per hour, and Pipe 2 fills at 1/24 per hour. Step 2: Calculate the combined work rate by adding the fractions: 1/8 + 1/24 = 3/24 + 1/24 = 4/24 = 1/6. Step 3: The reciprocal of the combined rate is 6, meaning the tank will be full in 6 hours.
195
Pipe A can fill a reservoir in 5 hours and Pipe B can fill it in 20 hours. How long will it take to fill the reservoir together?
Answer:
4 hours
Step 1: Formulate the hourly rates: 1/5 for Pipe A and 1/20 for Pipe B. Step 2: Add the rates: 1/5 + 1/20 = 4/20 + 1/20 = 5/20. Simplify the fraction to 1/4. Step 3: Since the combined rate is 1/4 of the reservoir per hour, the total time to fill it is 4 hours.
196
If Pipe X can fill a tank in 15 minutes and Pipe Y can fill it in 20 minutes, how much time will it take if both operate together?
Answer:
8 4/7 minutes
Step 1: Identify the per-minute work rate of each pipe: Pipe X = 1/15, Pipe Y = 1/20. Step 2: Add the rates together using a common denominator of 60: 4/60 + 3/60 = 7/60. Step 3: The time taken is the reciprocal of 7/60, which is 60/7 minutes. Converting this to a mixed fraction yields 8 4/7 minutes.
197
Pipe A fills a tank in 12 hours and Pipe B fills the same tank in 24 hours. Working together, in how many hours will the tank be full?
Answer:
8 hours
Step 1: Find the fraction of the tank filled by each pipe in one hour: Pipe A = 1/12, Pipe B = 1/24. Step 2: Sum these fractions to find the combined hourly rate: 1/12 + 1/24 = 2/24 + 1/24 = 3/24 = 1/8. Step 3: Invert the fraction 1/8 to find the total time required, which is exactly 8 hours.
198
A pipe can fill a pool in 4 hours, and another pipe can fill it in 12 hours. How long will it take to fill the pool if both are used together?
Answer:
3 hours
Step 1: Calculate the work rate of each pipe. Pipe 1 = 1/4 per hour, Pipe 2 = 1/12 per hour. Step 2: Add the rates to find the joint efficiency: 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3. Step 3: A combined rate of 1/3 means the entire pool will be filled in 3 hours.
199
Two pipes can fill a cistern in 20 hours and 30 hours respectively. If both are opened simultaneously, find the time taken to fill the cistern.
Answer:
12 hours
Step 1: The first pipe's filling rate is 1/20 per hour. The second pipe's filling rate is 1/30 per hour. Step 2: Combine their rates to find the total work done per hour: 1/20 + 1/30. The least common multiple (LCM) is 60. So, 3/60 + 2/60 = 5/60 = 1/12. Step 3: The reciprocal of the combined rate gives the total time. Thus, it takes 12 hours to fill the cistern.
200
Pipe A can fill a tank in 10 hours and Pipe B can fill it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?
Answer:
6 hours
Step 1: Determine the hourly rate of each pipe. Pipe A fills 1/10 of the tank per hour, and Pipe B fills 1/15 of the tank per hour. Step 2: Calculate their combined hourly rate by adding individual rates: 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Step 3: Since together they fill 1/6 of the tank in one hour, they will take exactly 6 hours to fill the entire tank.