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
181
A can do a piece of work in 10 days and B in 15 days. They work together for 2 days, and then A leaves. How many days will B take to finish the remaining work?
Answer:
10 days
Combined rate = 1/10 + 1/15 = 1/6. In 2 days, they complete 2*(1/6) = 1/3 of the work. Remaining work = 2/3. B's rate is 1/15. Time taken by B = (2/3) / (1/15) = 10 days.
182
A can do a piece of work in 24 days, B in 6 days, and C in 12 days. Working together, they will complete the same work in:
Answer:
3 3/7 days
Combined rate = 1/24 + 1/6 + 1/12 = (1 + 4 + 2)/24 = 7/24. Time taken = 24/7 = 3 3/7 days.
183
A and B can do a work in 8 days, B and C in 12 days, and A, B, and C together in 6 days. How long would A and C take to complete the work together?
Answer:
8 days
A+B+C = 1/6. A = (A+B+C) - (B+C) = 1/6 - 1/12 = 1/12. C = (A+B+C) - (A+B) = 1/6 - 1/8 = 1/24. A+C = 1/12 + 1/24 = 3/24 = 1/8. They take 8 days.
184
A and B together can do a work in 12 days, B and C in 15 days, and C and A in 20 days. In how many days can they complete the work if they all work together?
Answer:
10 days
2(A + B + C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5. So, A + B + C = 1/10. They will take 10 days to complete the work.
185
X, Y, and Z can independently finish a project in 20, 30, and 60 days respectively. How long will it take for them to finish the project if they all work together?
Answer:
10 days
Combined rate = 1/20 + 1/30 + 1/60 = (3 + 2 + 1)/60 = 6/60 = 1/10. Together, they will take 10 days to finish.
186
A, B, and C can complete a piece of work in 10, 12, and 15 days respectively. If they work together, in how many days will the work be finished?
Answer:
4 days
Combined 1 day's work = 1/10 + 1/12 + 1/15 = (6 + 5 + 4)/60 = 15/60 = 1/4. They will finish the work together in 4 days.
187
A can build a wall in 8 days, and B can build it in 12 days. Working together, how many days will it take them to build the wall?
Answer:
4.8 days
A's rate = 1/8, B's rate = 1/12. Combined rate = 1/8 + 1/12 = 5/24. Total time = 24/5 = 4.8 days.
188
P and Q together can do a piece of work in 8 days. If P alone takes 12 days to do it, how many days will Q take to do it alone?
Answer:
24 days
Combined rate = 1/8. P's rate = 1/12. Q's rate = (1/8) - (1/12) = (3-2)/24 = 1/24. Q will take 24 days to complete it alone.
189
A and B working together can complete a work in 12 days. If A alone can complete it in 20 days, in how many days can B alone complete the work?
Answer:
30 days
Combined rate (A+B) = 1/12. A's rate = 1/20. B's rate = (1/12) - (1/20) = (5-3)/60 = 2/60 = 1/30. So, B alone can complete it in 30 days.
190
If X can finish a job in 20 days and Y can finish the same job in 30 days, how long will they take to finish it together?
Answer:
12 days
X's rate = 1/20, Y's rate = 1/30. Combined rate = 1/20 + 1/30 = 3/60 + 2/60 = 5/60 = 1/12. Thus, they will finish the job in 12 days.