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
681
Person P can complete a project in 8 days. Person Q can complete the same project in 24 days. How many days will they take to complete the project working together?
Answer:
6 days
Step 1: The LCM of 8 and 24 is 24, which represents the total units of work. Step 2: P's efficiency is 24/8 = 3 units/day. Q's efficiency is 24/24 = 1 unit/day. Step 3: Their combined efficiency is 3 + 1 = 4 units/day. Total time required is 24/4 = 6 days.
682
A takes 15 days to do a job, and B takes 20 days. If they work together, how long will it take?
Answer:
8 4/7 days
Step 1: Let the total work be the LCM of 15 and 20, which is 60 units. Step 2: A's 1-day work is 60/15 = 4 units. B's 1-day work is 60/20 = 3 units. Step 3: Together they complete 4 + 3 = 7 units per day. The total time taken is 60/7 days, which is 8 4/7 days.
683
If X can build a wall in 20 days and Y can build the same wall in 30 days, how many days will it take for them to build it together?
Answer:
12 days
Step 1: The total work can be assumed as the LCM of 20 and 30, which is 60 units. Step 2: X builds 60/20 = 3 units/day. Y builds 60/30 = 2 units/day. Step 3: Their joint efficiency is 3 + 2 = 5 units/day. The time taken together is 60/5 = 12 days.
684
A can complete a task in 12 days, and B can complete it in 24 days. Working together, in how many days will they finish the task?
Answer:
8 days
Step 1: Let the total work be the LCM of 12 and 24, which is 24 units. Step 2: A's efficiency is 24/12 = 2 units/day. B's efficiency is 24/24 = 1 unit/day. Step 3: Their combined efficiency is 2 + 1 = 3 units/day. The time taken to finish the work is 24/3 = 8 days.
685
A can do a piece of work in 10 days and B can do the same work in 15 days. How long will they take if both work together?
Answer:
6 days
Step 1: Assume total work is the LCM of 10 and 15, which is 30 units. Step 2: Calculate the 1-day work (efficiency) of A and B. A does 30/10 = 3 units/day, and B does 30/15 = 2 units/day. Step 3: Together they do 3 + 2 = 5 units per day. The total time taken to complete 30 units is 30/5 = 6 days.
686
In what ratio should ingredients costing ₹23 and ₹40 per kg be mixed to obtain a mixture worth ₹33.5 per kg?
Answer:
6.5 : 10.5
Step-by-step solution: 1. Use the rule of allegation: (price2 - mean) : (mean - price1). 2. Required ratio = (40 - 33.5) : (33.5 - 23). 3. Therefore the ratio is 6.5 : 10.5.
687
In what ratio should ingredients costing ₹20 and ₹37 per kg be mixed to obtain a mixture worth ₹30.5 per kg?
Answer:
6.5 : 10.5
Step-by-step solution: 1. Use the rule of allegation: (price2 - mean) : (mean - price1). 2. Required ratio = (37 - 30.5) : (30.5 - 20). 3. Therefore the ratio is 6.5 : 10.5.
688
In what ratio should ingredients costing ₹20 and ₹41 per kg be mixed to obtain a mixture worth ₹32.5 per kg?
Answer:
8.5 : 12.5
Step-by-step solution: 1. Use the rule of allegation: (price2 - mean) : (mean - price1). 2. Required ratio = (41 - 32.5) : (32.5 - 20). 3. Therefore the ratio is 8.5 : 12.5.
689
In what ratio should ingredients costing ₹21 and ₹39 per kg be mixed to obtain a mixture worth ₹32.0 per kg?
Answer:
7.0 : 11.0
Step-by-step solution: 1. Use the rule of allegation: (price2 - mean) : (mean - price1). 2. Required ratio = (39 - 32.0) : (32.0 - 21). 3. Therefore the ratio is 7.0 : 11.0.
690
In what ratio should ingredients costing ₹22 and ₹40 per kg be mixed to obtain a mixture worth ₹33.0 per kg?
Answer:
7.0 : 11.0
Step-by-step solution: 1. Use the rule of allegation: (price2 - mean) : (mean - price1). 2. Required ratio = (40 - 33.0) : (33.0 - 22). 3. Therefore the ratio is 7.0 : 11.0.