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
111
A milkman mixes 20 liters of water with 80 liters of milk. After selling one-fourth of this mixture, he adds water to replenish the quantity that he had sold. What is the current proportion of water to milk?
Answer:
2:3
Step 1: Initial mixture = 100L. Milk = 80L, Water = 20L. Step 2: Sells 1/4th (25L). Remaining milk = 60L, Water = 15L. Step 3: Adds 25L water. New water = 40L. Milk = 60L. Ratio = 40 : 60 = 2 : 3.
112
In a 60 liter mixture of milk and water, the ratio of milk to water is 2:1. How much water must be added to make the ratio 1:2?
Answer:
60 liters
Step 1: Initial milk = 40L, water = 20L. Step 2: Target ratio milk:water = 1:2. Milk remains 40L. Step 3: So water should be 40 * 2 = 80L. Added water = 80 - 20 = 60 liters.
113
A liquid mixture contains 20% water and 80% acid. If 10 liters of water is added, the new mixture contains 30% water. What was the initial volume of the mixture?
Answer:
70 liters
Step 1: Acid amount is constant. Initial acid = 0.80 * V. Step 2: New volume = V + 10. New acid % = 70%. Step 3: 0.80V = 0.70(V + 10) -> 0.10V = 7 -> V = 70 liters.
114
A merchant buys two types of rice, one costing Rs. 20/kg and another Rs. 30/kg. He mixes them and sells the mixture at Rs. 28.80/kg, making a profit of 20%. In what ratio did he mix them?
Answer:
3:2
Step 1: CP of mixture = 28.80 / 1.2 = Rs. 24. Step 2: Mix 20 and 30 to get 24. Step 3: Ratio = (30 - 24) : (24 - 20) = 6 : 4 = 3 : 2.
115
How much water must be mixed with 14 liters of pure milk worth Rs. 5.40 per liter to yield a mixture worth Rs. 4.20 per liter?
Answer:
4 liters
Step 1: C = 0, D = 5.40, M = 4.20. Step 2: Ratio of water to milk = (5.40 - 4.20) : (4.20 - 0) = 1.20 : 4.20 = 2 : 7. Step 3: If 7 parts = 14 liters, then 2 parts = 4 liters.
116
The cost of two types of mixed fertilizers is Rs. 15/kg and Rs. 20/kg. If both are mixed in the ratio 2:3, what will be the price per kg of the mixed fertilizer?
Answer:
Rs. 18
Step 1: Weighted average formula. Step 2: Cost = (2 * 15 + 3 * 20) / (2 + 3). Step 3: (30 + 60) / 5 = 90 / 5 = Rs. 18.
117
A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.
Answer:
10 liters
Step 1: Let alcohol = 4x, water = 3x. Step 2: 4x / (3x + 5) = 4 / 5. Step 3: 20x = 12x + 20 -> 8x = 20 -> x = 2.5. Alcohol = 4x = 10 liters.
118
In a zoo, there are rabbits and pigeons. If heads are counted, there are 200 and if legs are counted, there are 580. How many pigeons are there?
Answer:
110
Step 1: Average legs per head = 580 / 200 = 2.9. Step 2: Pigeons have 2 legs, rabbits have 4. Alligation on 2 and 4 to get 2.9. Ratio of rabbits to pigeons = (2.9 - 2) : (4 - 2.9) = 0.9 : 1.1 = 9 : 11. Step 3: Total parts = 20. Pigeons = (11/20) * 200 = 110.
119
How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may on selling the mixture at 40 paise per kg gain 25%?
Answer:
20 kg
Step 1: CP of mixture = 40 / 1.25 = 32 paise. Step 2: Alligation of 42p and 24p to get 32p. Ratio = (32 - 24) : (42 - 32) = 8 : 10 = 4 : 5. Step 3: 4/5 = x / 25 -> x = 20 kg.
120
Two equal glasses are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a tumbler. The ratio of milk and water in the tumbler is:
Answer:
7:17
Step 1: Milk in glass 1 = 1/3, Water = 2/3. Milk in glass 2 = 1/4, Water = 3/4. Step 2: Total milk = 1/3 + 1/4 = 7/12. Total water = 2/3 + 3/4 = 17/12. Step 3: Ratio = 7/12 : 17/12 = 7 : 17.