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
171
A mixture of a certain quantity of milk with 16 liters of water is worth Rs. 3 per liter. If pure milk is worth Rs. 7 per liter, how much milk is there in the mixture?
Answer:
12 liters
Step 1: Cost of water = Rs. 0. Cost of milk = Rs. 7. Mean cost = Rs. 3. Step 2: Ratio of water to milk = (7 - 3) : (3 - 0) = 4 : 3. Step 3: Quantity of water is 16 liters. Let milk be x. 4/3 = 16/x. Therefore, x = 12 liters.
172
In what ratio must water be mixed with milk costing Rs. 12 per liter to obtain a mixture worth Rs. 8 per liter?
Answer:
1:2
Step 1: Cost of water is Rs. 0. Cost of milk is Rs. 12. Mean price is Rs. 8. Step 2: By alligation, Ratio = (12 - 8) : (8 - 0). Step 3: Ratio = 4 : 8 = 1 : 2.
173
A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is:
Answer:
600 kg
Step 1: Use alligation on profits: 8% and 18%, mean is 14%. Step 2: Ratio = (18 - 14) : (14 - 8) = 4 : 6 = 2 : 3. Step 3: Total parts = 2 + 3 = 5. Quantity at 18% profit = (3/5) * 1000 = 600 kg.
174
In what proportion must tea at Rs. 14 per kg be mixed with tea at Rs. 18 per kg so that the mixture is worth Rs. 17 per kg?
Answer:
1:3
Step 1: Apply alligation. Cheaper = 14, Dearer = 18, Mean = 17. Step 2: Ratio = (18 - 17) : (17 - 14). Step 3: Ratio = 1 : 3.
175
In what ratio must rice at Rs. 20 per kg be mixed with rice at Rs. 25 per kg so that the mixture is worth Rs. 22 per kg?
Answer:
3:2
Step 1: Use the rule of alligation. Cost of cheaper (C) = 20, Cost of dearer (D) = 25, Mean price (M) = 22. Step 2: Ratio of cheaper to dearer = (D - M) : (M - C). Step 3: (25 - 22) : (22 - 20) = 3 : 2.