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
621
If 5 men or 9 women can do a work in 19 days, then in how many days can 3 men and 6 women do the same work?
Answer:
15 days
Step 1: 5M = 9W. Target group is 3M + 6W. Step 2: Convert to women: 3M = 3*(9/5)W = 27/5 W. Total = 27/5 W + 30/5 W = 57/5 W. Step 3: 9W take 19 days, so 1W takes 171 days. Time for 57/5 W = 171 / (57/5) = 171 * 5 / 57 = 3 * 5 = 15 days.
622
1 man, 1 woman, and 1 boy can do a job in 20, 30, and 60 days respectively. How many boys must assist 2 men and 8 women to do the work in 2 days?
Answer:
8
Step 1: Total work = LCM(20, 30, 60) = 60. Efficiencies: 1M=3, 1W=2, 1B=1. Step 2: To finish in 2 days, the required total efficiency is 60 / 2 = 30 units/day. Step 3: Efficiency of 2M and 8W = 2(3) + 8(2) = 6 + 16 = 22. Required additional efficiency is 30 - 22 = 8. Since 1 boy = 1 unit/day, 8 boys are needed.
623
If 4 men or 6 boys can finish a job in 20 days, how many days will 6 men and 11 boys take?
Answer:
6 days
Step 1: 4M = 6B, meaning 2M = 3B. Step 2: Target group = 6M + 11B = 3(3B) + 11B = 9B + 11B = 20B. Step 3: 6B take 20 days, so 1B takes 120 days. Therefore, 20B take 120 / 20 = 6 days.
624
If 3 men or 4 women can complete a work in 43 days, how long will 7 men and 5 women take to complete it?
Answer:
12 days
Step 1: 3M = 4W, so 1M = 4/3 W. Step 2: Target group = 7M + 5W = 7(4/3 W) + 5W = 28/3 W + 15/3 W = 43/3 W. Step 3: 4W take 43 days, so 1W takes 172 days. Thus, (43/3)W take 172 / (43/3) = 172 * 3 / 43 = 4 * 3 = 12 days.
625
If 2 men or 3 women can do a piece of work in 15 days, in how many days can 6 men and 9 women do the same work?
Answer:
2.5 days
Step 1: Convert men to women: 2M = 3W, so 1M = 1.5W. Step 2: Convert the target group to women: 6M + 9W = 6(1.5W) + 9W = 9W + 9W = 18W. Step 3: Since 3W take 15 days, 1W takes 45 days. Therefore, 18W take 45/18 = 2.5 days.
626
A takes 9 days and B takes 12 days to complete a work. If they work on alternate days starting with B, the work will be completed in:
Answer:
10 1/3 days
Step 1: Total work = 36. A's eff = 4, B's eff = 3. Step 2: The cycle starts with B. 2-day cycle (B then A) yields 3 + 4 = 7 units. 5 cycles (10 days) yield 35 units. Remaining = 1 unit. Step 3: On the 11th day, it's B's turn. B takes 1/3 day to complete the 1 unit. Total time = 10 1/3 days.
627
A can do a work in 11 days, B in 22 days, and C in 33 days. A works daily, while B and C alternate to assist A. How many days will it take?
Answer:
7.75 days
Step 1: Total work = 66. A=6, B=3, C=2. Cycle is D1: A+B = 9 units, D2: A+C = 8 units. Step 2: A 2-day cycle yields 17 units. 3 cycles (6 days) yield 51 units. Remaining = 15 units. Step 3: Day 7: A+B does 9 units. Remaining = 6 units. Day 8: A+C takes 6/8 = 3/4 day. Total time = 7 3/4 (or 7.75) days.
628
A can do a work in 20 days, B in 15 days, and C in 12 days. A works daily, and is assisted by B and C on alternate days (i.e., A+B, then A+C). How many days will it take?
Answer:
8 days
Step 1: Total work = 60. A=3, B=4, C=5. Step 2: A is assisted by B and C on alternate days... wait, the question says 'assisted by B and C on alternate days' meaning D1=A+B+C? Or A works daily, B and C assist every alternate day? Let's assume D1: A works alone, D2: A+B+C. Then a 2-day cycle is A + (A+B+C) = 3 + 12 = 15 units. Step 3: To finish 60 units, it takes 60/15 = 4 cycles. 4 cycles * 2 days = 8 days.
629
A can do a work in 10 days, B in 20 days, and C in 30 days. A works daily, and is assisted by B and C on every third day. In how many days is the work completed?
Answer:
8 2/11 days
Step 1: Total work = 60. Efficiencies: A=6, B=3, C=2. Step 2: Consider a 3-day cycle. Day 1: A does 6. Day 2: A does 6. Day 3: A+B+C does 11. Total in 3 days = 23 units. Step 3: 2 cycles (6 days) yield 46 units. Remaining = 14 units. Day 7: A does 6. Day 8: A does 6. Remaining = 2. Day 9: A+B+C take 2/11 day. Total time = 8 2/11 days.
630
P takes 8 days and Q takes 12 days to complete a job. Working on alternate days starting with P, how long does it take?
Answer:
9.5 days
Step 1: Total work = 24. P's eff = 3, Q's eff = 2. Step 2: A 2-day cycle yields 5 units. 4 cycles (8 days) yield 20 units. Remaining = 4 units. Step 3: 9th day is P's turn, completes 3 units. Remaining = 1 unit. 10th day is Q's turn, takes 1/2 day. Total time = 8 + 1 + 0.5 = 9.5 days.