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
5181
A liquid mixture contains 20% water and 80% acid. If 10 liters of water is added, the new mixture contains 30% water. What was the initial volume of the mixture?
Answer:
70 liters
Step 1: Acid amount is constant. Initial acid = 0.80 * V. Step 2: New volume = V + 10. New acid % = 70%. Step 3: 0.80V = 0.70(V + 10) -> 0.10V = 7 -> V = 70 liters.
5182
A merchant buys two types of rice, one costing Rs. 20/kg and another Rs. 30/kg. He mixes them and sells the mixture at Rs. 28.80/kg, making a profit of 20%. In what ratio did he mix them?
Answer:
3:2
Step 1: CP of mixture = 28.80 / 1.2 = Rs. 24. Step 2: Mix 20 and 30 to get 24. Step 3: Ratio = (30 - 24) : (24 - 20) = 6 : 4 = 3 : 2.
5183
How much water must be mixed with 14 liters of pure milk worth Rs. 5.40 per liter to yield a mixture worth Rs. 4.20 per liter?
Answer:
4 liters
Step 1: C = 0, D = 5.40, M = 4.20. Step 2: Ratio of water to milk = (5.40 - 4.20) : (4.20 - 0) = 1.20 : 4.20 = 2 : 7. Step 3: If 7 parts = 14 liters, then 2 parts = 4 liters.
5184
The cost of two types of mixed fertilizers is Rs. 15/kg and Rs. 20/kg. If both are mixed in the ratio 2:3, what will be the price per kg of the mixed fertilizer?
Answer:
Rs. 18
Step 1: Weighted average formula. Step 2: Cost = (2 * 15 + 3 * 20) / (2 + 3). Step 3: (30 + 60) / 5 = 90 / 5 = Rs. 18.
5185
A mixture contains alcohol and water in the ratio 4:3. If 5 liters of water is added to the mixture, the ratio becomes 4:5. Find the quantity of alcohol in the given mixture.
Answer:
10 liters
Step 1: Let alcohol = 4x, water = 3x. Step 2: 4x / (3x + 5) = 4 / 5. Step 3: 20x = 12x + 20 -> 8x = 20 -> x = 2.5. Alcohol = 4x = 10 liters.
5186
In a zoo, there are rabbits and pigeons. If heads are counted, there are 200 and if legs are counted, there are 580. How many pigeons are there?
Answer:
110
Step 1: Average legs per head = 580 / 200 = 2.9. Step 2: Pigeons have 2 legs, rabbits have 4. Alligation on 2 and 4 to get 2.9. Ratio of rabbits to pigeons = (2.9 - 2) : (4 - 2.9) = 0.9 : 1.1 = 9 : 11. Step 3: Total parts = 20. Pigeons = (11/20) * 200 = 110.
5187
How many kg of salt at 42 paise per kg must a man mix with 25 kg of salt at 24 paise per kg so that he may on selling the mixture at 40 paise per kg gain 25%?
Answer:
20 kg
Step 1: CP of mixture = 40 / 1.25 = 32 paise. Step 2: Alligation of 42p and 24p to get 32p. Ratio = (32 - 24) : (42 - 32) = 8 : 10 = 4 : 5. Step 3: 4/5 = x / 25 -> x = 20 kg.
5188
Two equal glasses are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a tumbler. The ratio of milk and water in the tumbler is:
Answer:
7:17
Step 1: Milk in glass 1 = 1/3, Water = 2/3. Milk in glass 2 = 1/4, Water = 3/4. Step 2: Total milk = 1/3 + 1/4 = 7/12. Total water = 2/3 + 3/4 = 17/12. Step 3: Ratio = 7/12 : 17/12 = 7 : 17.
5189
A container contains 10 liters of pure wine. 1 liter of wine is drawn and replaced with water. This is done 3 times. What is the ratio of wine to water in the final mixture?
Answer:
729:271
Step 1: Wine left = 10 * (1 - 1/10)^3 = 10 * 0.729 = 7.29 liters. Step 2: Water = 10 - 7.29 = 2.71 liters. Step 3: Ratio = 7.29 : 2.71 = 729 : 271.
5190
What is the ratio in which two sugar solutions of 20% and 40% concentration respectively be mixed to get a solution of 28% concentration?
Answer:
3:2
Step 1: C = 20, D = 40, M = 28. Step 2: Ratio = (40 - 28) : (28 - 20). Step 3: Ratio = 12 : 8 = 3 : 2.