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
141
Pipe A fills a drum in 18 hours. A leak slows it down to 27 hours. How long will it take for the leak to empty the full drum?
Answer:
54 hours
Step 1: Filling rate is 1/18. Net rate is 1/27. Step 2: Leak rate = 1/18 - 1/27. Step 3: Using LCM 54, the equation is 3/54 - 2/54 = 1/54. The leak will empty the drum in 54 hours.
142
A tap takes 14 hours to fill a tank. A leak causes it to take 21 hours instead. How long does the leak take to empty the filled tank?
Answer:
42 hours
Step 1: The tap's rate is 1/14. The effective rate is 1/21. Step 2: The leak's rate = 1/14 - 1/21. Step 3: Find a common denominator (42): 3/42 - 2/42 = 1/42. Therefore, it takes 42 hours.
143
A water tank fills in 9 hours. A crack at the bottom causes it to take 12 hours. How much time is needed for the crack to empty the full tank?
Answer:
36 hours
Step 1: The normal filling rate is 1/9. The delayed filling rate is 1/12. Step 2: Crack's rate = 1/9 - 1/12. Step 3: Determine the difference using LCM 36: 4/36 - 3/36 = 1/36. The crack empties the tank in 36 hours.
144
A pipe fills a vessel in 15 hours. Due to leakage, it takes 20 hours. How long will the leak take to empty the full vessel?
Answer:
60 hours
Step 1: Filling rate is 1/15. Net rate with leak is 1/20. Step 2: Leak rate = 1/15 - 1/20. Step 3: Using a common denominator of 60: 4/60 - 3/60 = 1/60. The leak takes exactly 60 hours.
145
It normally takes 20 hours to fill a reservoir, but a leak increases the time to 25 hours. In how many hours can the leak empty the entire full reservoir?
Answer:
100 hours
Step 1: Identify the normal rate (1/20) and the effective rate (1/25). Step 2: The leak's rate is 1/20 - 1/25. Step 3: Convert to a common denominator (100): 5/100 - 4/100 = 1/100. The leak requires 100 hours to empty the reservoir.
146
A tank takes 4 hours to fill via a pipe. Due to a hole in the tank, it actually takes 5 hours. If the pipe is closed, how long will the hole take to empty the full tank?
Answer:
20 hours
Step 1: Set up the rate equation. Pipe rate = 1/4. Net rate = 1/5. Step 2: Hole's rate = 1/4 - 1/5. Step 3: Calculate the difference: 5/20 - 4/20 = 1/20. The hole will drain the tank in 20 hours.
147
A pool usually fills in 5 hours, but a drain causes it to take 6 hours to fill. If the pool is full, how long will the drain take to empty it completely?
Answer:
30 hours
Step 1: The regular filling rate is 1/5. The slowed filling rate is 1/6. Step 2: The rate of the drain is 1/5 - 1/6. Step 3: The calculation is 6/30 - 5/30 = 1/30. Thus, the drain empties the pool in 30 hours.
148
An inlet pipe fills a drum in 12 hours. However, a bottom leak extends the filling time to 16 hours. How long will the leak take to empty the full drum?
Answer:
48 hours
Step 1: Inlet rate = 1/12. Effective rate with leak = 1/16. Step 2: Leak rate = 1/12 - 1/16. Step 3: Find a common denominator (48). 4/48 - 3/48 = 1/48. The leak will empty the drum in 48 hours.
149
A cistern can be filled by a tap in 8 hours, but it takes 10 hours to fill because of a leak. In what time will the leak alone empty the full cistern?
Answer:
40 hours
Step 1: The rate of the tap is 1/8, and the effective net rate is 1/10. Step 2: The rate of the leak is the difference: 1/L = 1/8 - 1/10. Step 3: Using 40 as the common denominator: 5/40 - 4/40 = 1/40. The leak takes 40 hours to empty the cistern.
150
A pipe normally fills a tank in 10 hours. Due to a leak at the bottom, it takes 15 hours to fill. How long will the leak take to empty the full tank?
Answer:
30 hours
Step 1: The normal filling rate is 1/10. The effective rate with the leak is 1/15. Let the leak's emptying rate be 1/L. Step 2: We know that 1/10 - 1/L = 1/15. Rearranging gives 1/L = 1/10 - 1/15. Step 3: Calculate the difference: 3/30 - 2/30 = 1/30. The leak alone takes 30 hours to empty the tank.