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
111
Pipes A and B fill a cistern in 4 hours and 6 hours respectively. Alternating every hour starting with A, the time taken is:
Answer:
4 hours 40 mins
Step 1: 2-hour cycle fills 1/4 + 1/6 = 5/12. Two cycles (4 hours) fill 10/12, leaving 2/12. Step 2: A's turn. A's rate is 1/4 = 3/12. A finishes the 2/12 in (2/12)/(3/12) = 2/3 hours. Step 3: 2/3 hours = 40 minutes. Total time is 4 hours 40 minutes.
112
Pipe A fills a tank in 6 hours and Pipe B in 8 hours. On alternate hours starting with A, how long will it take?
Answer:
6.75 hours
Step 1: A 2-hour cycle fills 1/6 + 1/8 = 7/24. Three cycles (6 hours) fill 21/24, leaving 3/24. Step 2: In the 7th hour, A works. A's rate is 1/6 = 4/24. Step 3: A fills the remaining 3/24 in (3/24) / (4/24) = 3/4 hours. Total time = 6.75 hours.
113
Pipes A and B fill a tank in 12 hours and 15 hours. Operating alternately starting with A, what is the total time?
Answer:
13.25 hours
Step 1: 2-hour cycle fills 1/12 + 1/15 = 9/60. Six cycles (12 hours) fill 54/60, leaving 6/60. Step 2: In the 13th hour, A fills 1/12 (or 5/60), leaving 1/60. Step 3: In the 14th hour, B's rate is 1/15 (or 4/60). Time for B = (1/60) / (4/60) = 1/4 hour. Total time = 13.25 hours.
114
Pipe A fills a container in 10 hours and Pipe B in 20 hours. Opened on alternate hours starting with A, the filling time is:
Answer:
13 hours
Step 1: In a 2-hour cycle, they fill 1/10 + 1/20 = 3/20. Step 2: Six cycles (12 hours) fill 18/20. Remaining is 2/20 = 1/10. Step 3: A's turn comes next. A fills exactly 1/10 in 1 hour. Total time = 12 + 1 = 13 hours.
115
Pipes A and B can fill a tank in 16 hours and 24 hours. Alternating every hour starting with A, how long does it take?
Answer:
19 hours
Step 1: A 2-hour cycle fills 1/16 + 1/24 = 5/48. Step 2: Nine cycles (18 hours) fill 45/48, leaving 3/48. Step 3: In the 19th hour, A (whose rate is 1/16 = 3/48) completely fills the remaining space in exactly 1 hour. Total time = 19 hours.
116
Pipe A fills a pool in 15 hours and Pipe B in 20 hours. If opened on alternate hours starting with A, the total time is:
Answer:
17 hours
Step 1: Cycle of 2 hours fills 1/15 + 1/20 = 7/60. Step 2: Eight cycles (16 hours) will fill 8 * (7/60) = 56/60. The remaining part is 4/60 = 1/15. Step 3: In the 17th hour, it is A's turn. A fills exactly 1/15 in 1 hour. Total time = 17 hours.
117
Pipes A and B fill a tank in 20 hours and 30 hours respectively. Operated on alternate hours starting with A, the tank fills in:
Answer:
24 hours
Step 1: A 2-hour cycle completes 1/20 + 1/30 = 5/60 = 1/12 of the tank. Step 2: Since 1/12 goes evenly into 1, exactly 12 full cycles are needed. Step 3: Total time = 12 cycles * 2 hours/cycle = 24 hours.
118
Pipe A fills a cistern in 8 hours and Pipe B in 12 hours. If they are opened for alternate hours starting with A, how long will it take?
Answer:
9.5 hours
Step 1: In a 2-hour cycle, they fill 1/8 + 1/12 = 5/24. Four cycles (8 hours) will fill 20/24, leaving 4/24 (or 1/6) of the tank. Step 2: In the 9th hour, A fills 1/8 (or 3/24), leaving 1/24. Step 3: In the 10th hour, B takes (1/24) / (1/12) = 1/2 hour. Total time = 9.5 hours.
119
Pipes A and B can fill a tank in 12 hours and 18 hours respectively. If they operate on alternate hours starting with A, what is the total time taken?
Answer:
14 1/3 hours
Step 1: In 2 hours, A and B fill 1/12 + 1/18 = 5/36. Step 2: 7 full cycles (14 hours) fill 35/36. Remaining is 1/36. Step 3: It's A's turn. A's rate is 1/12 per hour. Time for A = (1/36) / (1/12) = 1/3 hour. Total time = 14 + 1/3 hours.
120
Pipe A fills a tank in 10 hours and Pipe B fills it in 15 hours. If they are opened on alternate hours starting with A, how long will it take to fill the tank?
Answer:
12 hours
Step 1: In a 2-hour cycle, A works for 1 hour and B for 1 hour. Total filled in 2 hours = 1/10 + 1/15 = 1/6 of the tank. Step 2: To fill the whole tank, we need 6 such cycles. Step 3: Total time = 6 cycles * 2 hours/cycle = 12 hours.