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
91
A can do a work in 20 days, B in 15 days, and C in 12 days. A works daily, and is assisted by B and C on alternate days (i.e., A+B, then A+C). How many days will it take?
Answer:
8 days
Step 1: Total work = 60. A=3, B=4, C=5. Step 2: A is assisted by B and C on alternate days... wait, the question says 'assisted by B and C on alternate days' meaning D1=A+B+C? Or A works daily, B and C assist every alternate day? Let's assume D1: A works alone, D2: A+B+C. Then a 2-day cycle is A + (A+B+C) = 3 + 12 = 15 units. Step 3: To finish 60 units, it takes 60/15 = 4 cycles. 4 cycles * 2 days = 8 days.
92
A can do a work in 10 days, B in 20 days, and C in 30 days. A works daily, and is assisted by B and C on every third day. In how many days is the work completed?
Answer:
8 2/11 days
Step 1: Total work = 60. Efficiencies: A=6, B=3, C=2. Step 2: Consider a 3-day cycle. Day 1: A does 6. Day 2: A does 6. Day 3: A+B+C does 11. Total in 3 days = 23 units. Step 3: 2 cycles (6 days) yield 46 units. Remaining = 14 units. Day 7: A does 6. Day 8: A does 6. Remaining = 2. Day 9: A+B+C take 2/11 day. Total time = 8 2/11 days.
93
P takes 8 days and Q takes 12 days to complete a job. Working on alternate days starting with P, how long does it take?
Answer:
9.5 days
Step 1: Total work = 24. P's eff = 3, Q's eff = 2. Step 2: A 2-day cycle yields 5 units. 4 cycles (8 days) yield 20 units. Remaining = 4 units. Step 3: 9th day is P's turn, completes 3 units. Remaining = 1 unit. 10th day is Q's turn, takes 1/2 day. Total time = 8 + 1 + 0.5 = 9.5 days.
94
A takes 20 days to do a piece of work and B takes 30 days. If they work on alternate days starting with B, what is the total time taken?
Answer:
24 days
Step 1: Total work = 60. A's eff = 3, B's eff = 2. Step 2: A 2-day cycle (B then A) yields 2 + 3 = 5 units. Step 3: To complete 60 units, 60/5 = 12 cycles are needed. 12 cycles * 2 days/cycle = 24 days.
95
X can do a job in 16 days and Y in 24 days. Working alternately starting with X, how many days will it take?
Answer:
19 days
Step 1: Total work = 48. X's eff = 3, Y's eff = 2. Step 2: A 2-day cycle yields 5 units. 9 cycles (18 days) yield 45 units. Remaining work = 3 units. Step 3: On the 19th day, it's X's turn. X finishes the 3 units in exactly 1 day. Total time = 19 days.
96
A can finish a work in 15 days and B in 20 days. If they work on alternate days starting with A, what is the total time taken?
Answer:
17 days
Step 1: Total work = 60. A's eff = 4, B's eff = 3. Step 2: A 2-day cycle yields 7 units. 8 cycles (16 days) yield 56 units. Remaining work = 4 units. Step 3: On the 17th day, it's A's turn. A's efficiency is 4, so A finishes the remaining work in exactly 1 day. Total time = 17 days.
97
A takes 12 days to complete a task and B takes 18 days. Working on alternate days starting with A, in how many days will the task be completed?
Answer:
14 1/3 days
Step 1: Total work = 36. A's eff = 3, B's eff = 2. Step 2: A 2-day cycle yields 5 units. 7 cycles (14 days) yield 35 units. Remaining work = 1 unit. Step 3: On the 15th day, it's A's turn. A takes 1/3 of a day to complete the remaining 1 unit. Total time = 14 + 1/3 days.
98
A can do a piece of work in 10 days and B in 15 days. How long will they take if they work on alternate days, starting with A?
Answer:
12 days
Step 1: Total work = 30. A's eff = 3, B's eff = 2. Step 2: In a 2-day cycle, the work done is 3 + 2 = 5 units. Step 3: To complete 30 units, they need 30/5 = 6 cycles. 6 cycles * 2 days/cycle = 12 days.
99
M takes 14 days and N takes 21 days to complete a job. N leaves 2 days before the job is finished. Total time taken is:
Answer:
9.2 days
Step 1: Total work = 42. M's eff = 3, N's eff = 2. Step 2: N leaves 2 days early, so M works alone for 2 days, completing 2 * 3 = 6 units. Step 3: Work done together = 42 - 6 = 36 units. Time taken together = 36 / 5 = 7.2 days. Total time = 7.2 + 2 = 9.2 days.
100
A can do a work in 20 days and B in 25 days. A leaves 3 days before the work finishes. What is the total time taken?
Answer:
12.77 days
Step 1: Total work = 100. A's eff = 5, B's eff = 4. Step 2: A leaves 3 days early, so B works alone for 3 days, completing 3 * 4 = 12 units. Step 3: Work done together = 100 - 12 = 88 units. Time taken together = 88 / 9 days. Total time = 88/9 + 3 = 115/9 = 12.77 days.