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
131
A tank is filled by Pipe A in 8 hours. Pipe B empties it at a rate of 3 liters per minute. Both open, the tank fills in 12 hours. What is the capacity?
Answer:
4320 liters
Step 1: Find the time for B to empty the tank. 1/8 - 1/B = 1/12 => 1/B = 1/8 - 1/12 = 3/24 - 2/24 = 1/24. B takes 24 hours. Step 2: Convert 24 hours to minutes: 24 * 60 = 1440 minutes. Step 3: Capacity = 1440 minutes * 3 liters/minute = 4320 liters.
132
Pipe A fills a tank in 20 hours. Pipe B empties the tank at 10 liters per hour. Working together, they fill the tank in 25 hours. What is the tank's capacity?
Answer:
1000 liters
Step 1: Let Pipe B empty the tank in B hours. 1/20 - 1/B = 1/25. Step 2: Calculate 1/B: 1/B = 1/20 - 1/25 = 5/100 - 4/100 = 1/100. B takes 100 hours to empty the tank. Step 3: Capacity = Time * Rate = 100 hours * 10 liters/hour = 1000 liters.
133
Pipe A fills a pool in 15 hours. Pipe B empties it at 5 liters per minute. Together they fill the pool in 20 hours. What is the capacity of the pool in liters?
Answer:
18000 liters
Step 1: Net rate equation is 1/15 - 1/B = 1/20. Solve for B: 1/B = 1/15 - 1/20 = 1/60. So, B empties the pool in 60 hours. Step 2: Convert B's time to minutes: 60 hours * 60 minutes = 3600 minutes. Step 3: Capacity = B's time in minutes * B's rate = 3600 * 5 = 18000 liters.
134
Pipe A fills a cistern in 12 hours. Pipe B empties it at 6 liters per hour. With both pipes open, the empty cistern fills in 20 hours. Find the cistern's capacity.
Answer:
180 liters
Step 1: Form the rate equation: 1/12 - 1/B = 1/20, where B is the time to empty the tank. Step 2: Solve for B: 1/B = 1/12 - 1/20 = 5/60 - 3/60 = 2/60 = 1/30. B empties it in 30 hours. Step 3: Capacity = 30 hours * 6 liters/hour = 180 liters.
135
Pipe A fills a tank in 10 hours. Pipe B empties water at a rate of 4 liters per hour. If the completely empty tank is filled in 15 hours with both pipes open, what is the capacity of the tank?
Answer:
120 liters
Step 1: Let B empty the tank in x hours. The net filling rate is 1/10 - 1/x = 1/15. Step 2: Solving for x gives 1/x = 1/10 - 1/15 = 1/30. So, B alone can empty the full tank in 30 hours. Step 3: Capacity = B's time * B's flow rate = 30 hours * 4 liters/hour = 120 liters.
136
Pipe A takes half the time of Pipe B to fill a tank. If they together fill it in 14 hours, how long will Pipe A take to fill it alone?
Answer:
21 hours
Step 1: Taking half the time means A is twice as fast as B. Let B's rate be 1x, then A's rate is 2x. Step 2: Combined rate is 3x. Total capacity = 3x * 14 = 42x. Step 3: Time for A alone = 42x / 2x = 21 hours.
137
Pipe A is 4 times as fast as Pipe B. Together they fill a pool in 8 hours. How long will it take Pipe B alone to fill the pool?
Answer:
40 hours
Step 1: Assume B's rate is 1 unit. A's rate is 4 units. Combined rate = 5 units. Step 2: The total capacity of the pool = 5 units/hour * 8 hours = 40 units. Step 3: Time for B alone = 40 units / 1 unit/hour = 40 hours.
138
Pipe A is twice as fast as Pipe B. If Pipe A alone takes 10 hours to fill the tank, how long will they take working together?
Answer:
6.67 hours
Step 1: Since A is twice as fast as B, B will take twice as long as A. B takes 20 hours. Step 2: Their combined hourly rate is 1/10 + 1/20 = 3/20. Step 3: The total time together is the reciprocal, 20/3 hours, which is approximately 6.67 hours.
139
Pipe A is 3 times as fast as Pipe B. Together they fill a cistern in 15 hours. How long will it take Pipe A alone to fill the cistern?
Answer:
20 hours
Step 1: Let the rate of B be x. The rate of A is 3x. Their combined rate is 4x. Step 2: The total work is the combined rate multiplied by time: 4x * 15 = 60x. Step 3: Time for A alone = Total work / A's rate = 60x / 3x = 20 hours.
140
Pipe A is twice as fast as Pipe B. Together they can fill a tank in 12 hours. How long will Pipe B alone take to fill the tank?
Answer:
36 hours
Step 1: Let B's filling speed be 1 unit per hour. Then A's speed is 2 units per hour. Step 2: Together, their speed is 3 units per hour. Since they take 12 hours together, total capacity = 3 * 12 = 36 units. Step 3: Time taken by B alone = Total capacity / B's speed = 36 / 1 = 36 hours.