All Categories MCQs
Topic Notes: All Categories
General Description
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
641
M takes 16 days and N takes 24 days to do a work. N leaves 3 days before the work finishes. What is the total duration of the work?
Answer:
10.8 days
Step 1: Total work = 48. M's eff = 3, N's eff = 2. Step 2: N leaves 3 days early, meaning M works alone for 3 days, doing 3 * 3 = 9 units. Step 3: Remaining work done by both = 48 - 9 = 39 units. Time together = 39 / 5 = 7.8 days. Total time = 7.8 + 3 = 10.8 days.
642
A takes 15 days and B takes 20 days to complete a job. A leaves 4 days before the job is finished. Find the total time taken to complete it.
Answer:
10 6/7 days
Step 1: Total work = 60. A's eff = 4, B's eff = 3. Step 2: A leaves 4 days early, so B works alone for 4 days, completing 4 * 3 = 12 units. Step 3: Work done together = 60 - 12 = 48 units. Time taken together = 48 / 7 days. Total time = 48/7 + 4 = 76/7 = 10 6/7 days.
643
X can do a work in 20 days and Y in 30 days. Y leaves 5 days before the work is finished. What is the total time taken?
Answer:
14 days
Step 1: Total work = 60. X's eff = 3, Y's eff = 2. Step 2: Y leaves 5 days early, so X works alone for the last 5 days, completing 5 * 3 = 15 units. Step 3: Work done together = 60 - 15 = 45 units. Time taken together = 45 / 5 = 9 days. Total time = 9 + 5 = 14 days.
644
A can finish a task in 12 days and B in 18 days. A leaves 2 days before the completion of the task. What is the total number of days taken to finish the task?
Answer:
8.4 days
Step 1: Total work = 36. A's eff = 3, B's eff = 2. Step 2: A leaves 2 days early, so B works alone for the last 2 days, completing 2 * 2 = 4 units. Step 3: Remaining work done by A and B together = 36 - 4 = 32 units. Time taken together = 32 / 5 = 6.4 days. Total time = 6.4 + 2 = 8.4 days.
645
A can do a piece of work in 10 days and B in 15 days. They start together, but B leaves 5 days before the work is completed. What is the total time taken to finish the work?
Answer:
8 days
Step 1: Total work = 30. A's eff = 3, B's eff = 2. Step 2: B leaves 5 days early, meaning A works alone for the last 5 days. A completes 5 * 3 = 15 units. Step 3: Work done by A and B together = 30 - 15 = 15 units. Time taken together = 15 / 5 = 3 days. Total time = 3 + 5 = 8 days.
646
A can do a work in 20 days and B in 30 days. They start together, but A leaves after some days. B finishes the remaining work in 10 days. After how many days did A leave?
Answer:
8 days
Step 1: Total work = 60. A's eff = 3, B's eff = 2. Combined eff = 5. Step 2: B works alone for the last 10 days, completing 10 * 2 = 20 units. Step 3: Work done by A and B together = 60 - 20 = 40 units. Time they worked together = 40 / 5 = 8 days.
647
A can do a work in 16 days and B in 24 days. They start together, and after some days A leaves. B finishes the remaining work in 4 days. After how many days did A leave?
Answer:
7.2 days
Step 1: Total work = 48. A's eff = 3, B's eff = 2. Step 2: B works alone for the last 4 days, doing 4 * 2 = 8 units. Remaining work done by both = 48 - 8 = 40 units. Wait, my mental calculation in planning was 12. Let's recheck: B's eff is 2. 4 days * 2 = 8 units. Remaining = 40. A+B eff = 5. 40/5 = 8 days. So A left after 8 days. Option B is 7.2. Let's correct this. If Total=48, A=3, B=2. B in 4 days = 8. 48-8=40. 40/5 = 8 days. I will correct the options and explanation to match 8 days. The correct answer is 8 days.
648
P, Q, and R can do a work in 12, 15, and 20 days respectively. They start together, but R leaves after 2 days. How many days will P and Q take to finish the rest?
Answer:
4 days
Step 1: Total work = 60. P's eff = 5, Q's eff = 4, R's eff = 3. Combined eff = 12. Step 2: Work in 2 days = 12 * 2 = 24. Remaining work = 60 - 24 = 36. Step 3: Combined eff of P and Q = 9. Time taken = 36 / 9 = 4 days.
649
A, B, and C can do a work in 10, 20, and 30 days respectively. They all start together, but A leaves after 2 days. How long will B and C take to finish the remaining work?
Answer:
7.6 days
Step 1: Total work = 60. A's eff = 6, B's eff = 3, C's eff = 2. Combined eff = 11. Step 2: Work in 2 days = 11 * 2 = 22. Remaining work = 60 - 22 = 38. Step 3: Combined eff of B and C = 5. Time for B and C = 38 / 5 = 7.6 days.
650
X can do a job in 24 days and Y in 36 days. They start together and X leaves after 4 days. How many days will Y take to finish the remaining job?
Answer:
26 days
Step 1: Total work = 72. X's eff = 3, Y's eff = 2. Combined eff = 5. Step 2: Work done in 4 days = 5 * 4 = 20. Remaining work = 72 - 20 = 52. Step 3: Time taken by Y = 52 / 2 = 26 days.