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
51
Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture containing spirit and water in the ratio 8:5.
Answer:
7:9
Step 1: Spirit in A = 5/7, in B = 7/13, target = 8/13. Step 2: Ratio = (8/13 - 7/13) : (5/7 - 8/13). Step 3: 1/13 : (65-56)/91 = 1/13 : 9/91 = 7 : 9.
52
A liquid A is lighter than water by 20% and liquid B is heavier than water by 30%. In what ratio should they be mixed to get a mixture which is as heavy as water?
Answer:
3:2
Step 1: Let water weight be 100. A = 80, B = 130. Mean = 100. Step 2: Ratio of A to B = (130 - 100) : (100 - 80). Step 3: Ratio = 30 : 20 = 3 : 2.
53
Find the ratio in which tea at Rs. 15/kg and Rs. 20/kg should be mixed to produce a mixture worth Rs. 16.50/kg.
Answer:
7:3
Step 1: Cheaper = 15, Dearer = 20, Mean = 16.50. Step 2: Ratio = (20 - 16.50) : (16.50 - 15) = 3.50 : 1.50. Step 3: Ratio = 7 : 3.
54
An alloy contains zinc and copper in the ratio 5:3 and another alloy contains zinc and copper in the ratio 2:1. If equal quantities of both alloys are melted together, the ratio of zinc to copper in the new alloy will be:
Answer:
31:17
Step 1: Alloy 1: Zinc = 5/8. Alloy 2: Zinc = 2/3. Total Zinc = 5/8 + 2/3 = 31/24. Step 2: Alloy 1: Copper = 3/8. Alloy 2: Copper = 1/3. Total Copper = 3/8 + 1/3 = 17/24. Step 3: Ratio = 31/24 : 17/24 = 31 : 17.
55
A milk vendor mixes water with milk and sells the mixture at the cost price of pure milk, thereby making a 25% profit. Find the percentage of water in the mixture.
Answer:
20%
Step 1: Profit of 25% when sold at CP implies ratio of water to milk is 25:100 = 1:4. Step 2: Total mixture = 5 parts. Step 3: Percentage of water = (1 / 5) * 100 = 20%.
56
In a zoo, there are some pigeons and some rabbits. If their heads are counted, these are 100. If their legs are counted, these are 320. How many pigeons are there?
Answer:
40
Step 1: Average legs per head = 320 / 100 = 3.2. Step 2: Pigeons = 2 legs, Rabbits = 4 legs. Mean = 3.2. Ratio of Rabbits to Pigeons = (3.2 - 2) : (4 - 3.2) = 1.2 : 0.8 = 3 : 2. Step 3: Total 5 parts. Pigeons = (2/5) * 100 = 40.
57
If an alloy contains copper and silver in the ratio 3:2, what percentage of the alloy is silver?
Answer:
40%
Step 1: Total parts = 3 + 2 = 5 parts. Step 2: Silver is 2 parts. Step 3: Percentage = (2 / 5) * 100% = 40%.
58
Two alloys A and B contain zinc and copper in the ratio 1:2 and 2:3 respectively. In what ratio should the two alloys be mixed to get a new alloy containing zinc and copper in the ratio 5:8?
Answer:
3:10
Step 1: Zinc in A = 1/3, B = 2/5, Target = 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.
59
A merchant has 120 kg of sugar, part of which he sells at 10% profit and the rest at 25% profit. He gains 15% on the whole. The quantity sold at 10% profit is:
Answer:
80 kg
Step 1: Alligation: 10% and 25%, Mean = 15%. Step 2: Ratio of 10% part to 25% part = (25 - 15) : (15 - 10) = 10 : 5 = 2 : 1. Step 3: Quantity at 10% = (2/3) * 120 = 80 kg.
60
15 liters of a mixture contains alcohol and water in the ratio 1:4. If 3 liters of water is mixed in it, the percentage of alcohol in the new mixture will be:
Answer:
16.66%
Step 1: Initial alcohol = (1/5) * 15 = 3 liters. Step 2: New total volume = 15 + 3 = 18 liters. Step 3: Percentage of alcohol = (3 / 18) * 100 = 100/6 % = 16.66%.