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
631
A takes 20 days to do a piece of work and B takes 30 days. If they work on alternate days starting with B, what is the total time taken?
Answer:
24 days
Step 1: Total work = 60. A's eff = 3, B's eff = 2. Step 2: A 2-day cycle (B then A) yields 2 + 3 = 5 units. Step 3: To complete 60 units, 60/5 = 12 cycles are needed. 12 cycles * 2 days/cycle = 24 days.
632
X can do a job in 16 days and Y in 24 days. Working alternately starting with X, how many days will it take?
Answer:
19 days
Step 1: Total work = 48. X's eff = 3, Y's eff = 2. Step 2: A 2-day cycle yields 5 units. 9 cycles (18 days) yield 45 units. Remaining work = 3 units. Step 3: On the 19th day, it's X's turn. X finishes the 3 units in exactly 1 day. Total time = 19 days.
633
A can finish a work in 15 days and B in 20 days. If they work on alternate days starting with A, what is the total time taken?
Answer:
17 days
Step 1: Total work = 60. A's eff = 4, B's eff = 3. Step 2: A 2-day cycle yields 7 units. 8 cycles (16 days) yield 56 units. Remaining work = 4 units. Step 3: On the 17th day, it's A's turn. A's efficiency is 4, so A finishes the remaining work in exactly 1 day. Total time = 17 days.
634
A takes 12 days to complete a task and B takes 18 days. Working on alternate days starting with A, in how many days will the task be completed?
Answer:
14 1/3 days
Step 1: Total work = 36. A's eff = 3, B's eff = 2. Step 2: A 2-day cycle yields 5 units. 7 cycles (14 days) yield 35 units. Remaining work = 1 unit. Step 3: On the 15th day, it's A's turn. A takes 1/3 of a day to complete the remaining 1 unit. Total time = 14 + 1/3 days.
635
A can do a piece of work in 10 days and B in 15 days. How long will they take if they work on alternate days, starting with A?
Answer:
12 days
Step 1: Total work = 30. A's eff = 3, B's eff = 2. Step 2: In a 2-day cycle, the work done is 3 + 2 = 5 units. Step 3: To complete 30 units, they need 30/5 = 6 cycles. 6 cycles * 2 days/cycle = 12 days.
636
M takes 14 days and N takes 21 days to complete a job. N leaves 2 days before the job is finished. Total time taken is:
Answer:
9.2 days
Step 1: Total work = 42. M's eff = 3, N's eff = 2. Step 2: N leaves 2 days early, so M works alone for 2 days, completing 2 * 3 = 6 units. Step 3: Work done together = 42 - 6 = 36 units. Time taken together = 36 / 5 = 7.2 days. Total time = 7.2 + 2 = 9.2 days.
637
A can do a work in 20 days and B in 25 days. A leaves 3 days before the work finishes. What is the total time taken?
Answer:
12.77 days
Step 1: Total work = 100. A's eff = 5, B's eff = 4. Step 2: A leaves 3 days early, so B works alone for 3 days, completing 3 * 4 = 12 units. Step 3: Work done together = 100 - 12 = 88 units. Time taken together = 88 / 9 days. Total time = 88/9 + 3 = 115/9 = 12.77 days.
638
A takes 18 days and B takes 27 days to finish a task. B leaves 2 days before completion. Find the total number of days taken to finish the task.
Answer:
11.6 days
Step 1: Total work = 54. A's eff = 3, B's eff = 2. Step 2: B leaves 2 days early, so A works alone for 2 days, doing 2 * 3 = 6 units. Step 3: Work done together = 54 - 6 = 48 units. Time taken together = 48 / 5 = 9.6 days. Total time = 9.6 + 2 = 11.6 days.
639
X, Y, and Z can finish a work in 24, 36, and 48 days. They start together, but Z leaves 4 days before completion. Find the total time taken.
Answer:
12 days
Step 1: Total work = 144. X's eff = 6, Y's eff = 4, Z's eff = 3. Step 2: Z leaves 4 days early, so X and Y work alone for the last 4 days. Work done by X and Y = (6+4) * 4 = 40 units. Step 3: Work done by all three = 144 - 40 = 104 units. Time taken by all three = 104 / 13 = 8 days. Total time = 8 + 4 = 12 days.
640
A, B, and C can do a work in 10, 12, and 15 days respectively. They begin together. A leaves 2 days before completion, and B leaves 3 days before completion. What is the total time taken?
Answer:
5.8 days
Step 1: Total work = 60. A's eff = 6, B's eff = 5, C's eff = 4. Let the total time be x days. Step 2: A works for x-2 days, B works for x-3 days, and C works for x days. Step 3: Equation: 6(x-2) + 5(x-3) + 4x = 60. 6x - 12 + 5x - 15 + 4x = 60. 15x - 27 = 60, 15x = 87, x = 87 / 15 = 5.8 days.