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 container contains 10 liters of pure wine. 1 liter of wine is drawn and replaced with water. This is done 3 times. What is the ratio of wine to water in the final mixture?
Answer:
729:271
Step 1: Wine left = 10 * (1 - 1/10)^3 = 10 * 0.729 = 7.29 liters. Step 2: Water = 10 - 7.29 = 2.71 liters. Step 3: Ratio = 7.29 : 2.71 = 729 : 271.
122
What is the ratio in which two sugar solutions of 20% and 40% concentration respectively be mixed to get a solution of 28% concentration?
Answer:
3:2
Step 1: C = 20, D = 40, M = 28. Step 2: Ratio = (40 - 28) : (28 - 20). Step 3: Ratio = 12 : 8 = 3 : 2.
123
In what ratio must a grocer mix tea at Rs. 60 per kg and Rs. 65 per kg so that selling the mixture at Rs. 68.20 per kg yields a 10% profit?
Answer:
3:2
Step 1: CP = 68.20 / 1.1 = 62. Step 2: Alligation with 60 and 65 to get 62. Step 3: Ratio = (65 - 62) : (62 - 60) = 3 : 2.
124
The average weight of a class of 40 students is 30 kg and the average weight of another class of 20 students is 15 kg. Find the average weight of both classes combined.
Answer:
25 kg
Step 1: Total weight of class 1 = 40 * 30 = 1200 kg. Step 2: Total weight of class 2 = 20 * 15 = 300 kg. Step 3: Average = (1200 + 300) / (40 + 20) = 1500 / 60 = 25 kg.
125
A beaker contains 100 liters of alcohol. 10 liters of alcohol is taken out and replaced by water. This is repeated one more time. Find the percentage of alcohol left.
Answer:
81%
Step 1: Initial V = 100. Removed R = 10. Operations n = 2. Step 2: Alcohol remaining = 100 * (1 - 10/100)^2 = 100 * (0.9)^2. Step 3: 100 * 0.81 = 81 liters. Since total volume is 100, it is 81%.
126
A mixture of 20 liters of milk and water contains 20% water. How many liters of water should be added to make it 25% water?
Answer:
4/3 liters
Step 1: Initial milk = 80% of 20 = 16 liters. Step 2: Target is 25% water, meaning 75% milk. Step 3: 75% of New Total = 16. New Total = 16 / 0.75 = 64/3 = 21.33 liters. Added water = 64/3 - 20 = 4/3 liters.
127
Pure milk costs Rs. 16 per liter. After adding water, the milkman sells the mixture at Rs. 15 per liter and thereby makes a profit of 25%. In what ratio does he mix water with milk?
Answer:
1:3
Step 1: CP of the mixture = 15 / 1.25 = Rs. 12 per liter. Step 2: Cost of water = 0. Cost of milk = 16. Mean cost = 12. Step 3: Ratio of water to milk = (16 - 12) : (12 - 0) = 4 : 12 = 1 : 3.
128
A bucket contains a mixture of two liquids A and B in the proportion 7:5. If 9 liters of the mixture is replaced by 9 liters of liquid B, the ratio becomes 7:9. How much of liquid A was there in the bucket?
Answer:
21 liters
Step 1: Let total volume be 12x. A = 7x, B = 5x. Step 2: 9L removed means 21/4 L of A removed. New A = 7x - 21/4. Since A remains 7 parts of the new 16 parts total, and total volume is unchanged at 12x. Step 3: 7x - 21/4 = (7/16) * 12x -> 7x - 21/4 = 21x/4 -> 7x/4 = 21/4 -> x = 3. Initial A = 7x = 21 liters.
129
A merchant lends Rs. 1000 in two parts, one at 8% and the other at 10% interest. If the yearly average interest is 9.2%, find the amount lent at 8%.
Answer:
400
Step 1: Use alligation: 8% and 10%, Mean = 9.2%. Step 2: Ratio = (10 - 9.2) : (9.2 - 8) = 0.8 : 1.2 = 2 : 3. Step 3: Total parts = 5. Amount at 8% = (2/5) * 1000 = Rs. 400.
130
How much water must be added to 60 liters of a solution containing 20% alcohol to make it a solution containing 15% alcohol?
Answer:
20 liters
Step 1: Initial alcohol = 20% of 60 = 12 liters. Step 2: Let x liters of water be added. Total volume = 60 + x. Step 3: 15% of (60 + x) = 12. 60 + x = 12 / 0.15 = 80. x = 20 liters.