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
151
A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?
Answer:
10 liters
Step 1: Initial wine = 80% of 150 = 120L. Water = 30L. Step 2: In the new mixture, water is 25%, meaning wine is 75%. Step 3: 75% of New Total = 120L -> New Total = 120 / 0.75 = 160L. Added water = 160 - 150 = 10 liters.
152
A container contains 40 liters of milk. From this container 4 liters of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Answer:
29.16 liters
Step 1: Initial volume = 40. Replacement = 4. Number of operations = 3. Step 2: Milk left = 40 * (1 - 4/40)^3. Step 3: 40 * (0.9)^3 = 40 * 0.729 = 29.16 liters.
153
Two alloys A and B contain gold and copper in the ratio 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be:
Answer:
7:5
Step 1: A has 7/9 gold. B has 7/18 gold. Mixed equally. Step 2: Gold in C = (7/9 + 7/18) / 2 = (14/18 + 7/18) / 2 = 21/36 = 7/12. Step 3: Therefore, the remaining 5/12 is copper. Ratio of gold to copper = 7 : 5.
154
A mixture of 30 liters contains milk and water in the ratio 7:3. How much water must be added to it so that the ratio of milk and water becomes 3:7?
Answer:
40 liters
Step 1: Initial milk = (7/10)*30 = 21L. Initial water = 9L. Step 2: Let x liters of water be added. New ratio = 21 / (9 + x) = 3 / 7. Step 3: 147 = 27 + 3x -> 120 = 3x -> x = 40 liters.
155
Find the ratio in which salt at Rs. 1.20 per kg must be mixed with salt at Rs. 2.40 per kg so that the mixture is worth Rs. 1.50 per kg.
Answer:
3:1
Step 1: C = 1.20, D = 2.40, M = 1.50. Step 2: Ratio of C to D = (2.40 - 1.50) : (1.50 - 1.20). Step 3: Ratio = 0.90 : 0.30 = 3 : 1.
156
An alloy of copper and bronze contains 20% copper. Another alloy contains 10% copper. In what ratio must they be mixed to get an alloy with 12% copper?
Answer:
1:4
Step 1: Copper % in first = 20, in second = 10. Target = 12. Step 2: Ratio = (12 - 10) : (20 - 12). Step 3: Ratio = 2 : 8 = 1 : 4.
157
A merchant has 50 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 8% profit is:
Answer:
20 kg
Step 1: Use alligation: 8% and 18%, Mean = 14%. Step 2: Ratio = (18 - 14) : (14 - 8) = 4 : 6 = 2 : 3. Step 3: Total parts = 5 = 50 kg. 1 part = 10 kg. Quantity at 8% = 2 parts = 20 kg.
158
The ratio of milk and water in a mixture is 3:2. If 4 liters of water is added to the mixture, the ratio becomes 3:3. What is the initial quantity of milk?
Answer:
12 liters
Step 1: Let initial milk = 3x and water = 2x. Step 2: Water added = 4L. New ratio = 3x / (2x + 4) = 3 / 3 = 1. Step 3: 3x = 2x + 4, so x = 4. Initial milk = 3x = 3 * 4 = 12 liters.
159
A container contains 50 liters of milk. From this container 5 liters of milk was taken out and replaced by water. This process was repeated further two times. How much milk is now contained by the container?
Answer:
36.45 liters
Step 1: Initial Volume V = 50. Amount replaced R = 5. Total operations n = 3. Step 2: Final amount = V * (1 - R/V)^n = 50 * (1 - 5/50)^3. Step 3: 50 * (0.9)^3 = 50 * 0.729 = 36.45 liters.
160
In what ratio must a grocer mix two varieties of sugar costing Rs. 20 and Rs. 30 per kg to get a mixture worth Rs. 24 per kg?
Answer:
3:2
Step 1: C = 20, D = 30, M = 24. Step 2: Ratio of cheaper to dearer = (30 - 24) : (24 - 20). Step 3: Ratio = 6 : 4 = 3 : 2.