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
4561
From a cask of milk containing 30 liters, 6 liters are drawn out and the cask is filled up with water. If the same process is repeated one more time, what will be the ratio of milk to water in the resulting mixture?
Answer:
16:9
Step 1: Milk left = 30 * (1 - 6/30)^2 = 30 * (4/5)^2 = 30 * 16/25 = 19.2 liters. Step 2: Water = 30 - 19.2 = 10.8 liters. Step 3: Ratio = 19.2 : 10.8 = 192 : 108 = 16 : 9.
4562
A merchant buys 40 kg of rice at Rs. 12.50 per kg and 30 kg of rice at Rs. 14 per kg. He mixes them and wants to earn 10% profit. At what price per kg should he sell the mixture?
Answer:
Rs. 14.46
Step 1: Total CP = (40 * 12.50) + (30 * 14) = 500 + 420 = 920. Step 2: CP per kg = 920 / 70 = 13.14. Step 3: Target SP = 13.14 * 1.10 = 14.457 = Rs. 14.46.
4563
In what proportion must water be mixed with spirit to gain 16.66% by selling it at cost price?
Answer:
1:6
Step 1: Gain = 16.66% = 1/6. Step 2: Since sold at cost price, the ratio of water to spirit must be equal to the gain fraction. Step 3: Ratio = 1 : 6.
4564
To a sugar solution of 3 liters containing 40% sugar, 1 liter of water is added. The percentage of sugar in the new solution is:
Answer:
30%
Step 1: Sugar amount = 40% of 3 = 1.2 liters. Step 2: New volume = 3 + 1 = 4 liters. Step 3: New percentage = (1.2 / 4) * 100 = 30%.
4565
A tank contains 100 liters of pure milk. 10 liters of milk is replaced with water, and this process is repeated twice more. Find the amount of pure milk left.
Answer:
72.9 liters
Step 1: V = 100, R = 10, n = 3. Step 2: Milk left = 100 * (1 - 10/100)^3 = 100 * 0.729. Step 3: Result is 72.9 liters.
4566
The ratio of copper and zinc in brass is 13:7. How much zinc will be there in 100 kg of brass?
Answer:
35 kg
Step 1: Total parts = 13 + 7 = 20. Step 2: 20 parts = 100 kg, so 1 part = 5 kg. Step 3: Zinc = 7 parts = 7 * 5 = 35 kg.
4567
In a mixture of 60 liters, the ratio of milk and water is 2:1. If this ratio is to be 1:2, then the quantity of water to be further added is:
Answer:
60 liters
Step 1: Initial milk = 40L, water = 20L. Step 2: Target ratio milk:water = 1:2. Milk remains 40L. Step 3: Target water = 80L. Added water = 80 - 20 = 60 liters.
4568
In what ratio must a person mix tea of Rs. 45 per kg and Rs. 50 per kg to make a mixture worth Rs. 48 per kg?
Answer:
2:3
Step 1: C = 45, D = 50, M = 48. Step 2: Ratio = (50 - 48) : (48 - 45). Step 3: Ratio = 2 : 3.
4569
A trader has 50 kg of pulses, part of which he sells at 14% profit and the rest at 6% loss. On the whole, his loss is 4%. What quantity is sold at 14% profit?
Answer:
5 kg
Step 1: Alligation: +14% and -6%, Mean = -4%. Step 2: Ratio of quantities = (-4 - (-6)) : (14 - (-4)) = 2 : 18 = 1 : 9. Step 3: Total parts = 10 = 50 kg. 1 part = 5 kg sold at 14% profit.
4570
Two containers have milk and water in the ratio 2:1 and 3:1 respectively. If both containers are emptied into a bigger container, find the ratio of milk to water in the bigger container if both original containers had the same volume.
Answer:
17:7
Step 1: Milk in A = 2/3, Water = 1/3. Milk in B = 3/4, Water = 1/4. Step 2: Total milk = 2/3 + 3/4 = 17/12. Total water = 1/3 + 1/4 = 7/12. Step 3: Ratio = 17 : 7.