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
671
P, Q, and R can complete a task in 15, 20, and 60 days respectively. If they work together, the task is completed in:
Answer:
7.5 days
Step 1: LCM(15, 20, 60) = 60 units. Step 2: P's efficiency = 4, Q's = 3, R's = 1. Step 3: Total efficiency = 4 + 3 + 1 = 8. Time taken = 60/8 = 7.5 days.
672
A, B, and C can do a job in 20, 24, and 30 days respectively. How long will it take if they work together?
Answer:
8 days
Step 1: Total work = LCM(20, 24, 30) = 120 units. Step 2: Efficiencies: A = 6, B = 5, C = 4. Step 3: Combined efficiency = 6 + 5 + 4 = 15. Time taken = 120/15 = 8 days.
673
Three workers can build a wall in 8, 12, and 24 days respectively. How many days will they take working together?
Answer:
4 days
Step 1: Let the total work be 24 units (LCM of 8, 12, 24). Step 2: Efficiencies are 24/8=3, 24/12=2, and 24/24=1. Step 3: Total efficiency is 3+2+1 = 6 units/day. Time taken = 24/6 = 4 days.
674
X, Y, and Z can do a work in 12, 15, and 20 days respectively. Working together, they will complete the work in:
Answer:
5 days
Step 1: Total work = LCM(12, 15, 20) = 60 units. Step 2: X's efficiency = 5, Y's = 4, Z's = 3. Step 3: Total combined efficiency = 5 + 4 + 3 = 12 units/day. Time = 60/12 = 5 days.
675
A, B, and C can complete a piece of work in 10, 12, and 15 days respectively. In how many days will they finish the work together?
Answer:
4 days
Step 1: Find the LCM of 10, 12, and 15, which is 60 units. Step 2: Efficiencies: A = 60/10 = 6, B = 60/12 = 5, C = 60/15 = 4. Step 3: Total efficiency = 6 + 5 + 4 = 15 units/day. Time taken = 60/15 = 4 days.
676
A completes a work in 9 days and B in 18 days. Working together, they will finish the work in:
Answer:
6 days
Step 1: Total work = LCM(9, 18) = 18 units. Step 2: A's efficiency = 18/9 = 2 units/day. B's efficiency = 18/18 = 1 unit/day. Step 3: Combined efficiency = 2 + 1 = 3 units/day. Total days = 18/3 = 6 days.
677
John can type a report in 24 hours, and Mary can type it in 48 hours. How long will it take if they type it together?
Answer:
16 hours
Step 1: Let the total work be the LCM of 24 and 48, which is 48 units. Step 2: John's rate is 48/24 = 2 units/hr. Mary's rate is 48/48 = 1 unit/hr. Step 3: Their joint rate is 3 units/hr. Time taken = 48/3 = 16 hours.
678
A can do a job in 5 days and B can do it in 20 days. In how many days can they complete the job together?
Answer:
4 days
Step 1: Total work is the LCM of 5 and 20, which is 20 units. Step 2: A completes 20/5 = 4 units/day, while B completes 20/20 = 1 unit/day. Step 3: Combined, they do 5 units/day. The time required is 20/5 = 4 days.
679
Worker M takes 18 days to paint a house, while Worker N takes 36 days. How long will they take working together?
Answer:
12 days
Step 1: The total work is the LCM of 18 and 36, which is 36 units. Step 2: M's rate is 36/18 = 2 units/day. N's rate is 36/36 = 1 unit/day. Step 3: Together, they paint 3 units a day. The total time taken is 36/3 = 12 days.
680
A can finish a work in 6 days and B can finish it in 12 days. If they work together, the work will be completed in:
Answer:
4 days
Step 1: Take the LCM of 6 and 12, which is 12 units. Step 2: Determine daily efficiencies: A does 12/6 = 2 units, and B does 12/12 = 1 unit. Step 3: Total efficiency is 2 + 1 = 3 units/day. The work is completed in 12/3 = 4 days.