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
241
What is the compounded ratio of (2 : 3), (4 : 5), and (6 : 7)?
Answer:
16 : 35
The compounded ratio of ratios (a:b), (c:d), and (e:f) is (a*c*e) : (b*d*f). Here, it is (2 * 4 * 6) : (3 * 5 * 7) = 48 : 105. Dividing both sides by 3 simplifies it to 16 : 35.
242
The sub-triplicate ratio of 64 : 125 is:
Answer:
4 : 5
The sub-triplicate ratio of a : b is the ratio of their cube roots. For 64 : 125, the cube root of 64 is 4, and the cube root of 125 is 5. Therefore, the ratio is 4 : 5.
243
The triplicate ratio of 2 : 3 is:
Answer:
8 : 27
The triplicate ratio of a : b is the ratio of their cubes, a^3 : b^3. For 2 : 3, the triplicate ratio is 2^3 : 3^3, which equals 8 : 27.
244
The sub-duplicate ratio of 16 : 49 is:
Answer:
4 : 7
The sub-duplicate ratio of two numbers a : b is the ratio of their square roots, sqrt(a) : sqrt(b). For 16 : 49, the sub-duplicate ratio is sqrt(16) : sqrt(49), which equals 4 : 7.
245
The duplicate ratio of 3 : 5 is:
Answer:
9 : 25
The duplicate ratio of two numbers a : b is the ratio of their squares, a^2 : b^2. For 3 : 5, the duplicate ratio is 3^2 : 5^2, which is 9 : 25.
246
If a : b = c : d, then which of the following is true?
Answer:
All of the above
These are standard properties of proportions. (a) is Componendo, (b) is Dividendo, and (c) is Componendo and Dividendo. If a/b = c/d, applying Componendo and Dividendo yields (a+b)/(a-b) = (c+d)/(c-d). All the given statements are correct transformations.
247
In a mixture of 60 liters, the ratio of milk to water is 2 : 1. How much water must be added to make the ratio 1 : 2?
Answer:
60 liters
Initial quantities: Milk = (2/3) * 60 = 40 L, Water = (1/3) * 60 = 20 L. Let x liters of water be added. The new ratio of milk to water is 40 / (20 + x) = 1 / 2. Cross-multiplying gives 80 = 20 + x, so x = 60. 60 liters of water must be added.
248
The ratio of the ages of a father and his son is 7 : 3. After 10 years, the ratio will be 2 : 1. Find the present age of the father.
Answer:
70 years
Let the present ages be 7x and 3x. After 10 years, (7x + 10) / (3x + 10) = 2 / 1. Cross-multiplying gives 7x + 10 = 6x + 20, which simplifies to x = 10. The present age of the father is 7x = 7 * 10 = 70 years.
249
A sum of money is divided among A, B, C, and D in the ratio 3 : 4 : 9 : 10. If the share of C is Rs. 2580 more than the share of B, what is the total amount of money?
Answer:
Rs. 13416
Let the shares be 3x, 4x, 9x, and 10x. Difference between C and B's share is 9x - 4x = 5x. Given 5x = 2580, so x = 516. The total amount is 3x + 4x + 9x + 10x = 26x. Total = 26 * 516 = Rs. 13416.
250
The salaries of A, B, and C are in the ratio 2 : 3 : 5. If their salaries are incremented by 15%, 10%, and 20% respectively, what will be the new ratio of their salaries?
Answer:
23 : 33 : 60
Let the salaries be 200, 300, and 500 for simplicity. New salary of A = 200 * 1.15 = 230. New salary of B = 300 * 1.10 = 330. New salary of C = 500 * 1.20 = 600. The new ratio is 230 : 330 : 600, which simplifies to 23 : 33 : 60.