All Categories MCQs
Topic Notes: All Categories
General Description
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
2541
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.
2542
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.
2543
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.
2544
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.
2545
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.
2546
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.
2547
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.
2548
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.
2549
There are 3 identical apples, 4 identical bananas, and 5 identical oranges in a basket. In how many ways can a person select at least one fruit?
Answer:
119
Step 1: Since items are identical, one can pick 0 to 3 apples (4 options), 0 to 4 bananas (5 options), and 0 to 5 oranges (6 options). Step 2: Total possible selections including the "empty" selection = 4 × 5 × 6 = 120. Step 3: Excluding the case where NO fruit is picked, valid selections = 120 - 1 = 119.
2550
What is the sum of all 3-digit numbers that can be formed using the digits 1, 2, and 3 without repetition?
Answer:
1332
Step 1: Number of such numbers is 3! = 6. Each digit appears in each place (hundreds, tens, units) exactly 2! = 2 times. Step 2: Sum of digits = 1 + 2 + 3 = 6. Step 3: Total sum = (Sum of digits) × (n-1)! × (111... n times) = 6 × 2 × 111 = 1332.