Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
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
131
Two vessels A and B contain a mixture of milk and water in the ratio 4:5 and 5:1. If both the vessels are mixed in the proportion 5:2, find the ratio of milk and water in the new mixture.
Answer:
5:4
Step 1: Milk in A = 4/9. Milk in B = 5/6. They are mixed in 5:2 ratio. Step 2: Milk in new mixture = (5 * 4/9 + 2 * 5/6) / 7 = (20/9 + 5/3) / 7 = (20/9 + 15/9) / 7 = 35/63 = 5/9. Step 3: Milk is 5/9, so water is 4/9. Ratio is 5:4.
132
A sum of Rs. 6.40 is made up of 80 coins which are either 10-paisa or 5-paisa coins. How many are 5-paisa coins?
Answer:
32
Step 1: Average value per coin = 640 paise / 80 = 8 paise. Step 2: Alligation on coins: 10p and 5p, mean is 8p. Ratio = (8 - 5) : (10 - 8) = 3 : 2. Step 3: Total parts = 5. Number of 5-paisa coins = (2/5) * 80 = 32.
133
In what ratio must a person mix tea at Rs. 27 per kg and Rs. 32 per kg so that the mixture costs Rs. 30 per kg?
Answer:
2:3
Step 1: Apply alligation. Cheaper = 27, Dearer = 32, Mean = 30. Step 2: Ratio = (32 - 30) : (30 - 27). Step 3: Ratio = 2 : 3.
134
A jar contains a mixture of two liquids A and B in the ratio 4:1. When 10 liters of the mixture is taken out and 10 liters of liquid B is poured into the jar, the ratio becomes 2:3. How many liters of liquid A was contained in the jar initially?
Answer:
16 liters
Step 1: Let initial volume be 5x. Liquid A is 4x. When 10L is removed, A removed = 8L. Remaining A = 4x - 8. Step 2: B removed = 2L. Remaining B = x - 2. After adding 10L of B, new B = x + 8. Step 3: New ratio = (4x - 8) / (x + 8) = 2/3. 12x - 24 = 2x + 16 -> 10x = 40 -> x = 4. Initial A = 4x = 16 liters.
135
An alloy contains copper, zinc, and nickel in the ratio 5:3:2. The quantity of nickel that must be added to 100 kg of this alloy to have the new ratio 5:3:3 is:
Answer:
10 kg
Step 1: Initial parts = 5 + 3 + 2 = 10 parts = 100 kg. So, 1 part = 10 kg. Step 2: The ratio of copper and zinc remains the same (5:3). The nickel parts increase from 2 to 3, an increase of 1 part. Step 3: 1 part = 10 kg. So, 10 kg of nickel must be added.
136
A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to this mixture to raise the percentage of water to 25%?
Answer:
4 kg
Step 1: Initial spirit = 90% of 20 = 18 kg. Step 2: In new mixture, spirit is 75%. Let total weight be W. 75% of W = 18 -> W = 18 / 0.75 = 24 kg. Step 3: Added water = 24 - 20 = 4 kg.
137
8 liters are drawn from a flask containing 64 liters of acid and replaced with water. This process is repeated 2 more times. What is the concentration of acid in the final mixture?
Answer:
66.99%
Step 1: Initial volume = 64L. Replacement = 8L. Operations = 3. Step 2: Final acid = 64 * (1 - 8/64)^3 = 64 * (7/8)^3 = 64 * 343 / 512 = 343 / 8 = 42.875 liters. Step 3: Concentration = (42.875 / 64) * 100 = 66.99%.
138
A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
Answer:
20%
Step 1: Gain is 25%, meaning ratio of water to milk is 25:100 = 1:4. Step 2: Total mixture = 1 + 4 = 5 parts. Step 3: Percentage of water = (1 / 5) * 100% = 20%.
139
In an alloy, zinc and copper are 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: Alloy 1 has Zinc = 1/3, Copper = 2/3. Alloy 2 has Zinc = 2/5, Copper = 3/5. Step 2: Since mixed equally, total Zinc = (1/3 + 2/5) = 11/15. Total Copper = (2/3 + 3/5) = 19/15. Step 3: Ratio = 11/15 : 19/15 = 11 : 19.
140
In what ratio must a person mix three kinds of tea costing Rs.60/kg, Rs.75/kg, and Rs.100/kg so that the resultant mixture when sold at Rs.96/kg yields a profit of 20%?
Answer:
1:4:2
Step 1: CP of mixture = 96 / 1.20 = Rs. 80. Step 2: Use double alligation. Mix 60 and 100 to get 80 -> Ratio = 20:20 = 1:1. Mix 75 and 100 to get 80 -> Ratio = 20:5 = 4:1. Step 3: Combine ratios. 60 : 75 : 100 = 1 : 4 : (1+1) = 1 : 4 : 2.