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
Pipes A and B can fill a tank in 6 hours and 8 hours respectively. After 2 hours, Pipe A is closed. How much time will Pipe B take to fill the remaining tank?
Answer:
3 hours 20 minutes
In 2 hours, work done = 2 * (1/6 + 1/8) = 2 * (7/24) = 14/24 = 7/12. Remaining = 5/12. Time taken by B = (5/12) / (1/8) = 10/3 hours = 3 hours 20 minutes.
142
Pipes A, B, and C can fill a tank in 10, 12, and 15 hours respectively. If all are opened together, in how many hours will the tank be full?
Answer:
4 hours
Combined rate = 1/10 + 1/12 + 1/15 = 15/60 = 1/4. They will fill it in 4 hours.
143
Pipe A can fill a tank in 8 hours, and Pipe B in 12 hours. Pipe A is opened for 2 hours, and then Pipe B is also opened. What is the total time taken to fill the tank?
Answer:
5.6 hours
In 2 hours, A fills 2/8 = 1/4 of the tank. Remaining = 3/4. Combined rate of A and B = 1/8 + 1/12 = 5/24. Time taken for remaining = (3/4) / (5/24) = 18/5 = 3.6 hours. Total time = 2 + 3.6 = 5.6 hours.
144
Pipe A fills a tank in 15 hours, Pipe B in 20 hours, and Pipe C empties it in 30 hours. If all three are opened, how long will it take to fill the tank?
Answer:
12 hours
Net rate = 1/15 + 1/20 - 1/30 = 4/60 + 3/60 - 2/60 = 5/60 = 1/12. It will take 12 hours to fill.
145
Pipe A can fill a tank in 12 hours, while Pipe B can empty the full tank in 20 hours. If both are opened together, how long will it take to fill the empty tank?
Answer:
30 hours
Net filling rate = 1/12 - 1/20 = (5 - 3)/60 = 2/60 = 1/30. The tank will be filled in 30 hours.
146
Pipe A can fill a tank in 10 hours and Pipe B can fill it in 15 hours. If both are opened together, how long will it take to fill the tank?
Answer:
6 hours
Rate of A = 1/10, Rate of B = 1/15. Combined rate = 1/10 + 1/15 = 5/30 = 1/6. The tank will be filled in 6 hours.
147
A can do a work in 8 days, and B in 10 days. With the help of C, they finish it in 4 days and earn Rs 8000. How much does C earn?
Answer:
Rs 800
Work done by C = 1/4 - (1/8 + 1/10) = 1/4 - 9/40 = 10/40 - 9/40 = 1/40. Efficiency ratio A:B:C = 1/8 : 1/10 : 1/40 = 5 : 4 : 1. C's share = (1/10) * 8000 = Rs 800.
148
A takes 5 days and B takes 7 days to complete a job. If they work together and earn Rs 1200, what is the difference between their shares?
Answer:
Rs 200
Efficiency ratio A:B = 7 : 5. Total parts = 12. Value of 1 part = 1200 / 12 = 100. Difference in parts = 7 - 5 = 2. Difference in shares = 2 * 100 = Rs 200.
149
A, B, and C complete a task and earn Rs 7500. A takes 10 days, B takes 12 days, and C takes 15 days to do it alone. What is A's share?
Answer:
Rs 3000
Efficiency ratio A:B:C = (1/10) : (1/12) : (1/15) = 6 : 5 : 4. Total parts = 15. A's share = (6/15) * 7500 = Rs 3000.
150
A can do a work in 20 days, and B in 30 days. With the help of C, they finish the work in 8 days. If they are paid Rs 6000 for the whole work, what is C's share?
Answer:
Rs 2000
C's 1 day work = 1/8 - (1/20 + 1/30) = 1/8 - 5/60 = 15/120 - 10/120 = 5/120 = 1/24. Ratio of efficiencies A:B:C = 1/20 : 1/30 : 1/24 = 6 : 4 : 5. C's share = (5/15) * 6000 = Rs 2000.