All Categories MCQs
Topic Notes: All Categories
General Description
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
4531
15 liters of a mixture contains alcohol and water in the ratio 1:4. If 3 liters of water is mixed in it, the percentage of alcohol in the new mixture will be:
Answer:
16.66%
Step 1: Initial alcohol = (1/5) * 15 = 3 liters. Step 2: New total volume = 15 + 3 = 18 liters. Step 3: Percentage of alcohol = (3 / 18) * 100 = 100/6 % = 16.66%.
4532
From a cask full of milk, 10 liters are taken out and replaced by water. This process is repeated twice. If the ratio of milk to water in the final mixture is 8:19, what is the capacity of the cask?
Answer:
30 liters
Step 1: Operations n=3. Milk/Total = 8 / (8+19) = 8/27. Step 2: 8/27 = (1 - 10/V)^3. Step 3: 2/3 = 1 - 10/V -> 10/V = 1/3 -> V = 30 liters.
4533
A mixture of 40 liters of milk and water contains 10% water. How much water should be added to this mixture so that the new mixture contains 20% water?
Answer:
5 liters
Step 1: Milk = 90% of 40 = 36L. Step 2: Target is 20% water, meaning 80% milk. Let V be new volume. 0.8V = 36 -> V = 45L. Step 3: Added water = 45 - 40 = 5 liters.
4534
A man buys milk at Rs. 5 per liter and after adding water sells it at Rs. 6 per liter, thereby making a profit of 33.33%. What is the proportion of water to milk in the mixture?
Answer:
1:9
Step 1: SP = 6, Profit = 1/3. CP of mixture = 6 / (4/3) = 18 / 4 = 4.5. Step 2: Alligation of Water (0) and Milk (5) to get 4.5. Step 3: Ratio = (5 - 4.5) : (4.5 - 0) = 0.5 : 4.5 = 1 : 9.
4535
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively so as to get a mixture worth Rs. 18 per kg?
Answer:
2:3
Step 1: C = 15, D = 20, M = 18. Step 2: Ratio = (20 - 18) : (18 - 15). Step 3: Ratio = 2 : 3.
4536
Two vessels contain mixtures of milk and water in the ratio of 4:1 and 9:11. If both are mixed in equal amounts, the ratio of milk to water in the resulting mixture is:
Answer:
25:15
Step 1: Milk in V1 = 4/5. Milk in V2 = 9/20. Step 2: Mixed equally: Milk = (4/5 + 9/20) / 2 = (16/20 + 9/20) / 2 = 25/40 = 5/8. Step 3: Milk is 5 parts, total is 8 parts. Water = 3 parts. Ratio = 5:3. Let's recheck options. 25:15 reduces to 5:3. Option B is correct.
4537
A vessel is full of a mixture of milk and water in which there is 15% water. How much mixture must be drawn off and replaced with water to make the water 25%?
Answer:
2/17
Step 1: Initial milk = 85%. Target milk = 75%. Step 2: Let x fraction be replaced. Milk left = 85% * (1 - x). Step 3: 0.85 * (1 - x) = 0.75 -> 1 - x = 75 / 85 = 15 / 17. x = 2 / 17.
4538
What proportion of water must be added to spirit to gain 25% by selling it at cost price?
Answer:
1:4
Step 1: Gain is 25%. Since it's sold at CP, the profit is exactly the amount of free water added. Step 2: Ratio of water to spirit = Profit % = 25% = 1/4. Step 3: Thus, ratio is 1:4.
4539
A mixture of 60 liters contains milk and water in the ratio 2:1. How much water must be added to make it 1:1?
Answer:
20 liters
Step 1: Initial milk = 40L, water = 20L. Step 2: Target is 1:1, meaning water must equal milk. Step 3: Water needed = 40L. Added water = 40 - 20 = 20 liters.
4540
A merchant has 2500 kg of rice, part of which he sells at 10% profit and the rest at 16% profit. He gains 12% on the whole. The quantity sold at 16% profit is:
Answer:
833.33 kg
Step 1: Alligation: 10% and 16%, Mean 12%. Step 2: Ratio of 10% part to 16% part = (16 - 12) : (12 - 10) = 4 : 2 = 2 : 1. Step 3: Quantity at 16% = (1/3) * 2500 = 833.33 kg.