Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
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
141
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.
142
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.
143
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.
144
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.
145
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.
146
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.
147
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.
148
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.