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
181
Find a fourth proportional to 12, 21, 8.
Answer:
14
12 : 21 :: 8 : x. 12x = 21 * 8 = 168. x = 168 / 12 = 14.
182
In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1:2:3. If there is Rs. 30 in all, how many 5 p coins are there?
Answer:
150
Let number of coins be x, 2x, 3x. Value in paise: 25x + 10(2x) + 5(3x) = 25x + 20x + 15x = 60x. Total value = 3000 paise. 60x = 3000 => x = 50. Number of 5 p coins = 3x = 150.
183
If 15% of x is the same as 20% of y, then x : y is:
Answer:
4 : 3
15x = 20y, so x/y = 20/15 = 4/3. Thus, x:y = 4:3.
184
Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is:
Answer:
4:5
Let third number be 100. First number = 120, Second number = 150. Ratio = 120:150 = 4:5.
185
A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?
Answer:
Rs. 2000
Ratio is 5x, 2x, 4x, 3x. C - D = 4x - 3x = x. Given x = 1000. B's share is 2x = 2000.
186
The ratio of present ages of A and B is 4:5. After 5 years, their ages will be in the ratio 5:6. What is the present age of A?
Answer:
20 years
Let present ages be 4x and 5x. (4x + 5) / (5x + 5) = 5 / 6. 24x + 30 = 25x + 25 => x = 5. Present age of A = 4x = 20 years.
187
If x/y = 3/4, then the value of (2x + 3y) / (3x - 2y) is:
Answer:
18 / 1
Substitute x=3 and y=4 directly: (2(3) + 3(4)) / (3(3) - 2(4)) = (6 + 12) / (9 - 8) = 18 / 1.
188
If a/b = 2/3 and b/c = 4/5, then (a + b) / (b + c) is equal to:
Answer:
20 / 27
Make b common: a:b = 8:12, b:c = 12:15. a=8k, b=12k, c=15k. (a + b) / (b + c) = (8k + 12k) / (12k + 15k) = 20k / 27k = 20 / 27.
189
In a mixture of 28 liters, the ratio of milk and water is 5 : 2. How much water should be added to make the ratio 2 : 5?
Answer:
42 liters
Initial milk = (5/7)*28 = 20 L. Initial water = (2/7)*28 = 8 L. Let x liters of water be added. 20 / (8 + x) = 2 / 5. 100 = 16 + 2x => 2x = 84 => x = 42 liters.
190
Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. Find the smaller number.
Answer:
49
Let numbers be 7x and 11x. (7x + 7) / (11x + 7) = 2 / 3. Cross-multiplying: 21x + 21 = 22x + 14 => x = 7. Smaller number is 7x = 7 * 7 = 49.