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
5161
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%.
5162
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.
5163
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.
5164
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.
5165
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.
5166
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.
5167
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.
5168
A tea merchant blends two varieties of tea costing Rs. 15 and Rs. 20 per kg in the ratio 2:3. He sells the blended tea at Rs. 21.60 per kg. His profit percent is:
Answer:
20%
Step 1: CP of mixture = (2 * 15 + 3 * 20) / 5 = (30 + 60) / 5 = Rs. 18. Step 2: SP = 21.60. Profit = 21.60 - 18 = 3.60. Step 3: Profit % = (3.60 / 18) * 100 = 20%.
5169
A vessel is full of a mixture of methanol and ethanol in which there is 20% ethanol. 10 liters of mixture are drawn off and filled with ethanol. If the ethanol is now 30%, what is the capacity of the vessel?
Answer:
80 liters
Step 1: Methanol is 80% initially. Target methanol is 70%. Step 2: Volume of methanol remains from the unremoved portion: 0.80 * (V - 10). Step 3: 0.80 * (V - 10) = 0.70 * V -> 0.8V - 8 = 0.7V -> 0.1V = 8 -> V = 80 liters.
5170
A mixture of 40 liters contains milk and water in the ratio 3:1. How much water must be added to it so that the ratio of milk and water becomes 2:1?
Answer:
5 liters
Step 1: Initial milk = (3/4)*40 = 30L. Initial water = 10L. Step 2: Target ratio is 2:1. Milk remains 30L. Step 3: Target water = 30 / 2 = 15L. Added water = 15 - 10 = 5 liters.