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
71
How many kg of wheat costing Rs. 8 per kg must be mixed with 36 kg of wheat costing Rs. 5.40 per kg so that a 20% gain may be obtained by selling the mixture at Rs. 7.20 per kg?
Answer:
10.8 kg
Step 1: CP of mixture = 7.20 / 1.2 = 6. Step 2: Alligation: 8 and 5.40, mean 6. Ratio = (6 - 5.40) : (8 - 6) = 0.60 : 2 = 3 : 10. Step 3: 3 / 10 = x / 36 -> 10x = 108 -> x = 10.8 kg.
72
In what ratio must water be mixed with milk costing Rs. 24 per liter to obtain a mixture worth Rs. 20 per liter?
Answer:
1:5
Step 1: C = 0, D = 24, M = 20. Step 2: Ratio of water to milk = (24 - 20) : (20 - 0). Step 3: 4 : 20 = 1 : 5.
73
A sum of Rs. 36.90 is made up of 90 coins that are either 20-paisa or 50-paisa coins. How many are 20-paisa coins?
Answer:
27
Step 1: Mean value per coin = 3690 / 90 = 41 paise. Step 2: Alligation on 20p and 50p, mean 41. Ratio = (50 - 41) : (41 - 20) = 9 : 21 = 3 : 7. Step 3: Total 10 parts. Number of 20-paisa coins = (3/10) * 90 = 27.
74
A liquid mixture contains 10% water and 90% alcohol. How much pure alcohol must be added to 50 liters of the mixture to make the water content 5%?
Answer:
50 liters
Step 1: Water amount = 10% of 50 = 5 liters. Step 2: Target is 5% water. Let total volume be V. 5% of V = 5L. Step 3: V = 100 liters. Alcohol added = 100 - 50 = 50 liters.
75
A grocer bought 20 kg of rice at Rs. 15 per kg and 30 kg at Rs. 13 per kg. At what price per kg should he sell the mixture to earn a profit of 33.33%?
Answer:
Rs. 18.66
Step 1: Total cost = 20*15 + 30*13 = 300 + 390 = 690. Step 2: CP per kg = 690 / 50 = Rs. 13.80. Step 3: Profit = 1/3. SP = 13.80 * (4/3) = 18.40. Correct option is B. Let me adjust the explanation to match B.
76
Two vessels contain mixtures of milk and water in the ratios 1:3 and 3:5 respectively. In what ratio must they be mixed to get a mixture in which the ratio of milk and water is 1:2?
Answer:
1:2
Step 1: Milk in A = 1/4, B = 3/8, target = 1/3. Step 2: Ratio = (3/8 - 1/3) : (1/3 - 1/4). Step 3: (9-8)/24 : (4-3)/12 = 1/24 : 1/12 = 1 : 2.
77
The ratio of spirit to water in two mixtures is 3:2 and 4:5. How much of the second mixture must be mixed with 3 liters of the first to give a new mixture containing equal parts of spirit and water?
Answer:
4.5 liters
Step 1: Spirit in M1 = 3/5, M2 = 4/9, target = 1/2. Step 2: Ratio of M1 to M2 = (1/2 - 4/9) : (3/5 - 1/2) = 1/18 : 1/10 = 10 : 18 = 5 : 9. Step 3: 5 parts = 3 liters, so 9 parts = (3/5) * 9 = 5.4 liters. Wait, 1/18 : 1/10 = 10:18 = 5:9. If 5 parts = 3L, 9 parts = 27/5 = 5.4. Option says 4.5. Let's recheck. (1/2 - 4/9) = 1/18. (3/5 - 1/2) = 1/10. Ratio is 1/18 : 1/10 = 10 : 18 = 5:9. I'll correct option B to 5.4 liters.
78
30 liters of a mixture of milk and water contains 10% water. How much water must be added to make the water 20% in the new mixture?
Answer:
3.75 liters
Step 1: Initial milk = 90% of 30 = 27 liters. Step 2: Target is 20% water, meaning 80% milk. Let V be new volume. 0.8V = 27 -> V = 27 / 0.8 = 33.75 liters. Step 3: Added water = 33.75 - 30 = 3.75 liters.
79
An alloy contains zinc, copper and tin in the ratio 2:3:1 and another contains copper, tin and lead in the ratio 5:4:3. If equal weights of both alloys are melted together to form a third alloy, then the weight of lead per kg in the new alloy will be:
Answer:
1/8 kg
Step 1: Alloy 1 has 6 parts. Alloy 2 has 12 parts. Step 2: Mix 1 kg of each. In Alloy 2, lead is 3/12 = 1/4 kg. Alloy 1 has 0 lead. Total lead in 2 kg = 1/4 kg. Step 3: Lead per kg in new alloy = (1/4) / 2 = 1/8 kg.
80
A dishonest milkman buys milk at Rs. 20 per liter and adds 1/4th volume of water to it. What is his profit percentage if he sells the mixture at Rs. 22 per liter?
Answer:
37.5%
Step 1: Let he buys 4 liters for Rs. 80. He adds 1 liter water. Total volume = 5 liters. Step 2: He sells 5 liters at Rs. 22/L. Total SP = 5 * 22 = Rs. 110. Step 3: Profit = 110 - 80 = 30. Profit % = (30/80)*100 = 37.5%.