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
101
A vessel is full of a mixture of methanol and ethanol in which there is 20% ethanol. 10 liters of mixture are drawn off and filled with ethanol. If the ethanol is now 30%, what is the capacity of the vessel?
Answer:
80 liters
Step 1: Methanol is 80% initially. Target methanol is 70%. Step 2: Volume of methanol remains from the unremoved portion: 0.80 * (V - 10). Step 3: 0.80 * (V - 10) = 0.70 * V -> 0.8V - 8 = 0.7V -> 0.1V = 8 -> V = 80 liters.
102
A mixture of 40 liters contains milk and water in the ratio 3:1. How much water must be added to it so that the ratio of milk and water becomes 2:1?
Answer:
5 liters
Step 1: Initial milk = (3/4)*40 = 30L. Initial water = 10L. Step 2: Target ratio is 2:1. Milk remains 30L. Step 3: Target water = 30 / 2 = 15L. Added water = 15 - 10 = 5 liters.
103
How much water must be added to 50 liters of pure milk worth Rs. 10 per liter to reduce its average price to Rs. 8 per liter?
Answer:
12.5 liters
Step 1: Water cost = 0, Milk = 10, Mean = 8. Step 2: Ratio of water to milk = (10 - 8) : (8 - 0) = 2 : 8 = 1 : 4. Step 3: 4 parts = 50 liters. 1 part = 50 / 4 = 12.5 liters.
104
If 2 kg of metal, of which 1/3 is zinc and the rest copper, is mixed with 3 kg of metal, of which 1/4 is zinc and the rest copper, what is the ratio of zinc to copper in the mixture?
Answer:
17:43
Step 1: Zinc in M1 = 2 * (1/3) = 2/3. Zinc in M2 = 3 * (1/4) = 3/4. Total Zinc = 2/3 + 3/4 = 17/12. Step 2: Copper in M1 = 4/3. Copper in M2 = 9/4. Total Copper = 4/3 + 9/4 = 43/12. Step 3: Ratio = 17/12 : 43/12 = 17 : 43.
105
A sum of Rs. 118 was divided among 50 boys and girls such that each boy gets Rs. 2.60 and each girl Rs. 1.80. Find the number of boys.
Answer:
35
Step 1: Mean = 118 / 50 = Rs. 2.36. Step 2: Boys = 2.60, Girls = 1.80, Mean = 2.36. Ratio = (2.36 - 1.80) : (2.60 - 2.36) = 0.56 : 0.24 = 7 : 3. Step 3: Total parts = 10. Number of boys = (7/10) * 50 = 35.
106
In what ratio should water be added to a liquid costing Rs. 15 per liter so as to make a profit of 20% by selling the diluted liquid at Rs. 15 per liter?
Answer:
1:5
Step 1: SP = 15, Profit = 20%. CP of mixture = 15 / 1.2 = 12.5. Step 2: Alligation with Water (0) and Liquid (15) to get 12.5. Step 3: Ratio = (15 - 12.5) : (12.5 - 0) = 2.5 : 12.5 = 1 : 5.
107
Two solutions of 90% and 97% purity are mixed resulting in 21 liters of mixture of 94% purity. How much is the quantity of the first solution in the resulting mixture?
Answer:
9 liters
Step 1: C = 90, D = 97, M = 94. Step 2: Ratio = (97 - 94) : (94 - 90) = 3 : 4. Step 3: Total parts = 7 = 21 liters. Quantity of first solution = (3/7) * 21 = 9 liters.
108
A merchant sells an item at 10% profit and another at 20% profit. If his overall profit on the combined cost price of Rs. 6000 is 14%, find the cost price of the item sold at 20% profit.
Answer:
2400
Step 1: Alligation: 10% and 20%, Mean = 14%. Step 2: Ratio of CP = (20 - 14) : (14 - 10) = 6 : 4 = 3 : 2. Step 3: Amount at 20% is 2 parts out of 5. CP = (2/5) * 6000 = Rs. 2400.
109
A vessel contains 60 liters of pure milk. 6 liters of milk is taken out and replaced with water. This process is repeated twice more. Find the amount of milk left.
Answer:
43.74 liters
Step 1: V = 60, R = 6, n = 3. Step 2: Milk left = 60 * (1 - 6/60)^3 = 60 * (0.9)^3. Step 3: 60 * 0.729 = 43.74 liters.
110
Find the ratio in which two alloys containing zinc and copper in the ratio 1:2 and 2:3 respectively must be mixed to get an alloy with zinc and copper in the ratio 5:8.
Answer:
3:10
Step 1: Zinc in A = 1/3. Zinc in B = 2/5. Target Zinc = 5/13. Step 2: Ratio = (2/5 - 5/13) : (5/13 - 1/3). Step 3: (26-25)/65 : (15-13)/39 = 1/65 : 2/39 = 39 : 130 = 3 : 10.