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
121
A and B together can do a piece of work in 12 days. If A is twice as fast as B, how long will B take alone to complete the work?
Answer:
36 days
Step 1: Efficiency ratio A:B = 2:1. Total efficiency = 3 units/day. Step 2: Total work = Combined efficiency * time = 3 * 12 = 36 units. Step 3: Time taken by B = Total work / B's efficiency = 36 / 1 = 36 days.
122
X is 60% more efficient than Y. If Y alone can do a work in 40 days, how long will X alone take?
Answer:
25 days
Step 1: Efficiency ratio of X:Y = 160:100 = 8:5. Step 2: Total work = Y's efficiency * Y's time = 5 * 40 = 200 units. Step 3: Time taken by X = Total work / X's efficiency = 200 / 8 = 25 days.
123
A is 20% more efficient than B. If A alone finishes a work in 30 days, in how many days can B alone finish it?
Answer:
36 days
Step 1: Efficiency of A to B is 120:100, or 6:5. Step 2: Total work = A's efficiency * A's time = 6 * 30 = 180 units. Step 3: Time taken by B = Total work / B's efficiency = 180 / 5 = 36 days.
124
A is thrice as good a workman as B and takes 60 days less than B to complete a piece of work. How long will they take working together?
Answer:
22.5 days
Step 1: Time ratio A:B = 1:3. Let A take x days and B take 3x days. Step 2: The difference is 3x - x = 2x. We are given 2x = 60, so x = 30. A takes 30 days and B takes 90 days. Step 3: Total work = LCM(30, 90) = 90. Combined efficiency = 3 + 1 = 4. Time together = 90/4 = 22.5 days.
125
A is twice as good a workman as B and therefore takes 10 days less than B to finish a job. In how many days can A alone finish the job?
Answer:
10 days
Step 1: Efficiency ratio A:B = 2:1. Therefore, the time ratio is 1:2. Step 2: Let A take x days and B take 2x days. The difference is 2x - x = x days. Step 3: We are given that x = 10. Thus, A takes 10 days alone.
126
A is 50% more efficient than B. If B alone takes 30 days to finish a task, how long will A take alone?
Answer:
20 days
Step 1: Efficiency ratio of A:B is 150:100, which simplifies to 3:2. Step 2: Total work = B's efficiency * B's time = 2 * 30 = 60 units. Step 3: Time taken by A alone = Total work / A's efficiency = 60 / 3 = 20 days.
127
A is thrice as fast as B. If they complete a work together in 15 days, how many days will B take alone to finish it?
Answer:
60 days
Step 1: Efficiency ratio of A:B is 3:1. Total efficiency = 3 + 1 = 4 units/day. Step 2: Total work = 4 units/day * 15 days = 60 units. Step 3: Time taken by B alone = Total work / B's efficiency = 60 / 1 = 60 days.
128
A is twice as fast as B. Together they can finish a piece of work in 14 days. How many days will A alone take to finish the work?
Answer:
21 days
Step 1: Efficiency ratio of A:B is 2:1. Total efficiency = 2 + 1 = 3 units/day. Step 2: Total work = Combined efficiency * time = 3 * 14 = 42 units. Step 3: Time taken by A alone = Total work / A's efficiency = 42 / 2 = 21 days.
129
A, B, and C can do a work in 16, 32, and 48 days respectively. Together they will take:
Answer:
8 8/11 days
Step 1: LCM(16, 32, 48) = 96 units. Step 2: A's efficiency = 6, B's = 3, C's = 2. Step 3: Total efficiency = 6 + 3 + 2 = 11. Time = 96/11 = 8 8/11 days.
130
P, Q, and R can complete a job in 12, 24, and 36 days respectively. In how many days can they complete the job together?
Answer:
6 6/11 days
Step 1: Total work = LCM(12, 24, 36) = 72 units. Step 2: Efficiencies: P = 6, Q = 3, R = 2. Step 3: Combined efficiency = 6 + 3 + 2 = 11. Time taken = 72/11 = 6 6/11 days.