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
101
A takes 18 days and B takes 27 days to finish a task. B leaves 2 days before completion. Find the total number of days taken to finish the task.
Answer:
11.6 days
Step 1: Total work = 54. A's eff = 3, B's eff = 2. Step 2: B leaves 2 days early, so A works alone for 2 days, doing 2 * 3 = 6 units. Step 3: Work done together = 54 - 6 = 48 units. Time taken together = 48 / 5 = 9.6 days. Total time = 9.6 + 2 = 11.6 days.
102
X, Y, and Z can finish a work in 24, 36, and 48 days. They start together, but Z leaves 4 days before completion. Find the total time taken.
Answer:
12 days
Step 1: Total work = 144. X's eff = 6, Y's eff = 4, Z's eff = 3. Step 2: Z leaves 4 days early, so X and Y work alone for the last 4 days. Work done by X and Y = (6+4) * 4 = 40 units. Step 3: Work done by all three = 144 - 40 = 104 units. Time taken by all three = 104 / 13 = 8 days. Total time = 8 + 4 = 12 days.
103
A, B, and C can do a work in 10, 12, and 15 days respectively. They begin together. A leaves 2 days before completion, and B leaves 3 days before completion. What is the total time taken?
Answer:
5.8 days
Step 1: Total work = 60. A's eff = 6, B's eff = 5, C's eff = 4. Let the total time be x days. Step 2: A works for x-2 days, B works for x-3 days, and C works for x days. Step 3: Equation: 6(x-2) + 5(x-3) + 4x = 60. 6x - 12 + 5x - 15 + 4x = 60. 15x - 27 = 60, 15x = 87, x = 87 / 15 = 5.8 days.
104
M takes 16 days and N takes 24 days to do a work. N leaves 3 days before the work finishes. What is the total duration of the work?
Answer:
10.8 days
Step 1: Total work = 48. M's eff = 3, N's eff = 2. Step 2: N leaves 3 days early, meaning M works alone for 3 days, doing 3 * 3 = 9 units. Step 3: Remaining work done by both = 48 - 9 = 39 units. Time together = 39 / 5 = 7.8 days. Total time = 7.8 + 3 = 10.8 days.
105
A takes 15 days and B takes 20 days to complete a job. A leaves 4 days before the job is finished. Find the total time taken to complete it.
Answer:
10 6/7 days
Step 1: Total work = 60. A's eff = 4, B's eff = 3. Step 2: A leaves 4 days early, so B works alone for 4 days, completing 4 * 3 = 12 units. Step 3: Work done together = 60 - 12 = 48 units. Time taken together = 48 / 7 days. Total time = 48/7 + 4 = 76/7 = 10 6/7 days.
106
X can do a work in 20 days and Y in 30 days. Y leaves 5 days before the work is finished. What is the total time taken?
Answer:
14 days
Step 1: Total work = 60. X's eff = 3, Y's eff = 2. Step 2: Y leaves 5 days early, so X works alone for the last 5 days, completing 5 * 3 = 15 units. Step 3: Work done together = 60 - 15 = 45 units. Time taken together = 45 / 5 = 9 days. Total time = 9 + 5 = 14 days.
107
A can finish a task in 12 days and B in 18 days. A leaves 2 days before the completion of the task. What is the total number of days taken to finish the task?
Answer:
8.4 days
Step 1: Total work = 36. A's eff = 3, B's eff = 2. Step 2: A leaves 2 days early, so B works alone for the last 2 days, completing 2 * 2 = 4 units. Step 3: Remaining work done by A and B together = 36 - 4 = 32 units. Time taken together = 32 / 5 = 6.4 days. Total time = 6.4 + 2 = 8.4 days.
108
A can do a piece of work in 10 days and B in 15 days. They start together, but B leaves 5 days before the work is completed. What is the total time taken to finish the work?
Answer:
8 days
Step 1: Total work = 30. A's eff = 3, B's eff = 2. Step 2: B leaves 5 days early, meaning A works alone for the last 5 days. A completes 5 * 3 = 15 units. Step 3: Work done by A and B together = 30 - 15 = 15 units. Time taken together = 15 / 5 = 3 days. Total time = 3 + 5 = 8 days.
109
A can do a work in 20 days and B in 30 days. They start together, but A leaves after some days. B finishes the remaining work in 10 days. After how many days did A leave?
Answer:
8 days
Step 1: Total work = 60. A's eff = 3, B's eff = 2. Combined eff = 5. Step 2: B works alone for the last 10 days, completing 10 * 2 = 20 units. Step 3: Work done by A and B together = 60 - 20 = 40 units. Time they worked together = 40 / 5 = 8 days.
110
A can do a work in 16 days and B in 24 days. They start together, and after some days A leaves. B finishes the remaining work in 4 days. After how many days did A leave?
Answer:
7.2 days
Step 1: Total work = 48. A's eff = 3, B's eff = 2. Step 2: B works alone for the last 4 days, doing 4 * 2 = 8 units. Remaining work done by both = 48 - 8 = 40 units. Wait, my mental calculation in planning was 12. Let's recheck: B's eff is 2. 4 days * 2 = 8 units. Remaining = 40. A+B eff = 5. 40/5 = 8 days. So A left after 8 days. Option B is 7.2. Let's correct this. If Total=48, A=3, B=2. B in 4 days = 8. 48-8=40. 40/5 = 8 days. I will correct the options and explanation to match 8 days. The correct answer is 8 days.