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
151
Pipes A and B can fill a tank in 30 hours and 45 hours respectively. Both are opened for 6 hours, then B is closed. What is the total time taken to fill the tank?
Answer:
26 hours
Step 1: Combined rate = 1/30 + 1/45 = 5/90 = 1/18. In 6 hours, they fill 6 * (1/18) = 1/3 of the tank. Step 2: The remaining 2/3 is filled by A alone. Time taken by A = (2/3) * 30 = 20 hours. Step 3: The total time taken from the start is 6 + 20 = 26 hours.
152
Pipes A and B can fill a tank in 20 hours and 25 hours respectively. Both are opened for 5 hours, and then A is closed. What is the total time taken to fill the entire tank?
Answer:
18.75 hours
Step 1: In 5 hours, A and B fill 5 * (1/20 + 1/25) = 5 * (9/100) = 45/100 = 9/20 of the tank. Step 2: The remaining part is 11/20. Pipe B takes (11/20) * 25 = 275/20 = 55/4 = 13.75 hours to fill the rest. Step 3: The total time taken to fill the tank is 5 hours + 13.75 hours = 18.75 hours.
153
Two pipes A and B can fill a tank in 15 hours and 30 hours respectively. If both are opened together, after what time should B be closed so the tank fills in exactly 12 hours?
Answer:
6 hours
Step 1: Pipe A runs for the full 12 hours. The work done by A is 12 * (1/15) = 12/15 = 4/5 of the tank. Step 2: The remaining 1/5 of the tank must have been filled by Pipe B. Step 3: Time B operated = (1/5) * 30 = 6 hours. Therefore, B must be closed after 6 hours.
154
Pipe A fills a tank in 24 hours, and Pipe B fills it in 36 hours. Both are opened simultaneously. After how many hours should B be closed to fill the tank in exactly 16 hours?
Answer:
12 hours
Step 1: Pipe A runs for the entire 16 hours. Work done by A = 16 * (1/24) = 16/24 = 2/3. Step 2: The remaining 1/3 of the tank must be filled by Pipe B. Step 3: Time taken by B to fill 1/3 is (1/3) * 36 = 12 hours. So, B should be closed after 12 hours.
155
Pipes A and B fill a tank in 12 hours and 18 hours. Both are opened simultaneously. After how many hours should Pipe A be closed so the tank is filled in exactly 10 hours?
Answer:
5.33 hours
Step 1: Pipe B runs for the full 10 hours. Work done by B = 10 * (1/18) = 10/18 = 5/9. Step 2: The remaining 4/9 of the tank must be filled by Pipe A. Step 3: Time taken by A = (4/9) * 12 = 48/9 = 16/3 = 5.33 hours. A should be closed after 5.33 hours.
156
Pipe A fills a tank in 10 hours and Pipe B in 20 hours. Both are opened simultaneously. After how many hours should Pipe A be closed so that the tank fills in exactly 8 hours?
Answer:
6 hours
Step 1: The tank is supposed to fill in 8 hours, and Pipe B runs for the entire 8 hours. Work done by B = 8 * (1/20) = 8/20 = 2/5. Step 2: The remaining 3/5 of the tank must be filled by Pipe A. Step 3: Time taken by A to fill 3/5 of the tank = (3/5) * 10 = 6 hours. Therefore, A must be closed after 6 hours.
157
Pipes A and B can fill a pool in 15 and 20 hours respectively. They are opened for 6 hours, then B is closed. How much time will A take to fill the remaining pool?
Answer:
4.5 hours
Step 1: Combined rate = 1/15 + 1/20 = 7/60. In 6 hours, they fill 6 * (7/60) = 7/10 of the pool. Step 2: Remaining pool to fill is 1 - 7/10 = 3/10. Step 3: A's rate is 1/15. Time for A = (3/10) * 15 = 45/10 = 4.5 hours.
158
Pipes A and B can fill a tank in 20 hours and 30 hours respectively. Both are opened for 4 hours, then A is closed. How much time will B take to fill the remaining tank?
Answer:
20 hours
Step 1: A and B's combined rate = 1/20 + 1/30 = 5/60 = 1/12. In 4 hours, they fill 4 * (1/12) = 1/3 of the tank. Step 2: Remaining tank = 1 - 1/3 = 2/3. Step 3: B's rate is 1/30. Time for B = (2/3) * 30 = 20 hours.
159
Pipe A fills a tank in 12 hours and B in 16 hours. Both are opened for 3 hours, after which B is closed. How much time will A take to fill the remaining tank?
Answer:
6.75 hours
Step 1: Combined rate = 1/12 + 1/16 = 7/48. In 3 hours, they fill 3 * (7/48) = 7/16 of the tank. Step 2: The remaining part is 1 - 7/16 = 9/16. Step 3: Pipe A's rate is 1/12. Time taken by A for the rest = (9/16) / (1/12) = (9/16) * 12 = 108/16 = 27/4 = 6.75 hours.
160
Pipes A and B can fill a tank in 10 hours and 15 hours respectively. Both are opened for 2 hours, and then A is closed. How long will it take for B to fill the rest of the tank?
Answer:
10 hours
Step 1: Combined rate of A and B is 1/10 + 1/15 = 1/6. In 2 hours, they fill 2 * (1/6) = 1/3 of the tank. Step 2: The remaining part of the tank to be filled is 1 - 1/3 = 2/3. Step 3: Pipe B's rate is 1/15. Time taken by B to fill the remaining 2/3 is (2/3) / (1/15) = (2/3) * 15 = 10 hours.