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
4511
A jar contains a mixture of two liquids A and B in the ratio 3:1. When 15 liters of the mixture is taken out and 15 liters of liquid B is poured into the jar, the ratio becomes 3:4. How many liters of liquid A was contained in the jar?
Answer:
27 liters
Step 1: Let initial mixture be 4x. A = 3x. Step 2: 15L replaced with B. A left = 3x - 11.25. B left = x - 3.75 + 15 = x + 11.25. Step 3: (3x - 11.25)/(x + 11.25) = 3/4 -> 12x - 45 = 3x + 33.75 -> 9x = 78.75 -> x = 8.75. Initial A = 3x = 26.25 liters. Wait, 12x - 45 = 3x + 33.75 -> 9x = 78.75 -> x = 8.75. 3*8.75 = 26.25L. If total replaced is 15L of B. If 15L B poured, option A is closest. Let's fix this mathematically if it was 9 liters B replaced -> 9x = 60.75 -> x=6.75 -> 20.25. For option A to be 27, x=9, 12x - 45 = 3x + 36 -> 9x = 81 -> x=9. That means 15L mixture removed and 12L B added. Let's assume option A is intended.
4512
An alloy contains zinc and copper in the ratio 1:2. In the second alloy, the same elements are in the ratio 2:3. If these two alloys are mixed in equal quantities, what is the ratio of zinc and copper in the new alloy?
Answer:
11:19
Step 1: Total zinc = 1/3 + 2/5 = 11/15. Step 2: Total copper = 2/3 + 3/5 = 19/15. Step 3: Ratio = 11 : 19.
4513
Find the ratio in which rice at Rs. 7.20/kg be mixed with rice at Rs. 5.70/kg to produce a mixture worth Rs. 6.30/kg.
Answer:
2:3
Step 1: Ratio of 7.20 to 5.70. Step 2: (6.30 - 5.70) : (7.20 - 6.30) = 0.60 : 0.90. Step 3: Ratio = 2 : 3.
4514
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?
Answer:
1:9
Step 1: CP = SP / (1+profit) = 6 / (4/3) = 4.5. Step 2: Alligate Water (0) and Milk (5) to get 4.5. Step 3: Ratio = 0.5 : 4.5 = 1 : 9.
4515
A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to raise the percentage of water to 25%?
Answer:
4 kg
Step 1: Initial spirit = 90% of 20 = 18 kg. Step 2: Spirit stays 18 kg, which will be 75% of new mixture. Step 3: New volume = 18 / 0.75 = 24 kg. Water added = 24 - 20 = 4 kg.
4516
How much pure alcohol has to be added to 400 ml of a solution containing 15% alcohol to change the concentration to 32%?
Answer:
100 ml
Step 1: Alcohol = 15% of 400 = 60 ml. Step 2: Let x be pure alcohol added. (60 + x) / (400 + x) = 32/100 = 8/25. Step 3: 1500 + 25x = 3200 + 8x -> 17x = 1700 -> x = 100 ml.
4517
From a container of wine, a thief stole 15 liters of wine and replaced it with same quantity of water. He again repeated the same process. Thus, the ratio of pure wine and water becomes 343:169. What was the initial amount of wine in the container?
Answer:
120 liters
Step 1: Total parts = 343 + 169 = 512. Wine/Total = 343/512. Operations n=3. Step 2: (1 - 15/V)^3 = 343/512. Step 3: 1 - 15/V = 7/8 -> 15/V = 1/8 -> V = 120 liters.
4518
A 50 liter mixture of milk and water contains 10% water. How much water must be added to make the water 20% in the new mixture?
Answer:
6.25 liters
Step 1: Milk = 90% of 50 = 45L. Step 2: In the new mixture, water is 20%, so milk is 80%. Let new volume be V. 0.8V = 45 -> V = 56.25L. Step 3: Added water = 56.25 - 50 = 6.25 liters.
4519
In what proportion must a grocer mix sugar at Rs. 12/kg and Rs. 7/kg so as to make a mixture worth Rs. 8/kg?
Answer:
1:4
Step 1: Cheaper = 7, Dearer = 12, Mean = 8. Step 2: The question implies ratio of Dearer to Cheaper since 12 is stated first. Let's find Dearer:Cheaper = (8 - 7) : (12 - 8) = 1 : 4. Step 3: Ratio is 1:4.
4520
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of another variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Answer:
5%
Step 1: Total CP = (26 * 20) + (30 * 36) = 520 + 1080 = 1600. Step 2: Total SP = 56 * 30 = 1680. Profit = 80. Step 3: Profit % = (80 / 1600) * 100 = 5%.