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
581
A can do a piece of work in 16 days and B in 19 days. In how many days can they complete it together?
Answer:
8.69
Step-by-step solution: 1. A's work rate = 1/16. 2. B's work rate = 1/19. 3. Combined rate = 1/16 + 1/19. 4. Time = 1 / combined rate = 8.69 days.
582
A can do a piece of work in 12 days and B in 21 days. In how many days can they complete it together?
Answer:
7.64
Step-by-step solution: 1. A's work rate = 1/12. 2. B's work rate = 1/21. 3. Combined rate = 1/12 + 1/21. 4. Time = 1 / combined rate = 7.64 days.
583
A can do a piece of work in 17 days and B in 20 days. In how many days can they complete it together?
Answer:
9.19
Step-by-step solution: 1. A's work rate = 1/17. 2. B's work rate = 1/20. 3. Combined rate = 1/17 + 1/20. 4. Time = 1 / combined rate = 9.19 days.
584
A can do a piece of work in 14 days and B in 25 days. In how many days can they complete it together?
Answer:
8.97
Step-by-step solution: 1. A's work rate = 1/14. 2. B's work rate = 1/25. 3. Combined rate = 1/14 + 1/25. 4. Time = 1 / combined rate = 8.97 days.
585
A can do a piece of work in 14 days and B in 20 days. In how many days can they complete it together?
Answer:
8.24
Step-by-step solution: 1. A's work rate = 1/14. 2. B's work rate = 1/20. 3. Combined rate = 1/14 + 1/20. 4. Time = 1 / combined rate = 8.24 days.
586
If 2 men or 4 women or 6 boys can do a work in 22 days, how long will 1 man, 1 woman, and 1 boy together take?
Answer:
24 days
Step 1: Establish equivalence: 2M = 4W = 6B, which means 1M = 3B and 1W = 1.5B. Step 2: Target group is 1M + 1W + 1B = 3B + 1.5B + 1B = 5.5B. Step 3: Since 6B take 22 days, total work = 132 B-days. Time taken by 5.5B = 132 / 5.5 = 24 days.
587
A, B, and C can do a work in 24, 30, and 40 days. They begin together but C leaves 4 days before completion. Total time taken is:
Answer:
11 days
Step 1: Total work = 120. Efficiencies: A=5, B=4, C=3. Step 2: Let total time be x. 5x + 4x + 3(x-4) = 120. Step 3: 12x - 12 = 120, 12x = 132, x = 11 days.
588
A is 3 times as efficient as B and therefore takes 40 days less than B to complete a work. How many days will B alone take?
Answer:
60 days
Step 1: Efficiency ratio is 3:1. Time ratio is 1:3. Step 2: Difference in time parts is 3 - 1 = 2 parts. We are given 2 parts = 40 days, so 1 part = 20 days. Step 3: B takes 3 parts of time, which is 3 * 20 = 60 days.
589
A can do a work in 10 days, B in 12 days, and C in 15 days. They all start together, but A leaves after 2 days, and B leaves 3 days before completion. Total time taken is:
Answer:
7 days
Step 1: Total work = 60. A=6, B=5, C=4. All three work for first 2 days: 2*(15) = 30 units. Remaining = 30. Step 2: After A leaves, B and C work. B leaves 3 days before the end, so C works alone for the last 3 days: 3*4=12 units. Remaining = 30 - 12 = 18. Step 3: These 18 units were done by B and C together. Time = 18/(5+4) = 2 days. Total time = 2 (all) + 2 (B+C) + 3 (C alone) = 7 days.
590
A does 4/5 of a piece of work in 20 days. He then calls in B and they finish the remaining work in 3 days. How long would B alone take to do the whole work?
Answer:
37.5 days
Step 1: A's total time = 20 * (5/4) = 25 days. The remaining work is 1/5. Step 2: A and B do 1/5 of the work in 3 days, so A+B's total time = 15 days. Step 3: Let Total work = 75. A's eff = 3, A+B's eff = 5. B's eff = 2. Time for B alone = 75 / 2 = 37.5 days.