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
251
A bag contains coins of 1 Rupee, 50 paise, and 25 paise in the ratio 2 : 3 : 4. If the total amount in the bag is Rs. 45, find the number of 50 paise coins.
Answer:
30
Let the number of 1 Rs, 50p, and 25p coins be 2x, 3x, and 4x respectively. Their values in Rupees are 2x * 1, 3x * 0.50, and 4x * 0.25. The total value is 2x + 1.5x + x = 4.5x. Given 4.5x = 45, so x = 10. Number of 50p coins = 3x = 30.
252
Two numbers are in the ratio 3 : 5. If 9 is subtracted from each, the new ratio becomes 12 : 23. What is the smaller number?
Answer:
33
Let the numbers be 3x and 5x. According to the question, (3x - 9) / (5x - 9) = 12 / 23. Cross-multiplying: 23(3x - 9) = 12(5x - 9) => 69x - 207 = 60x - 108 => 9x = 99 => x = 11. The smaller number is 3x = 3 * 11 = 33.
253
If 2A = 3B = 4C, then A : B : C is:
Answer:
6 : 4 : 3
Let 2A = 3B = 4C = k. Then A = k/2, B = k/3, C = k/4. The ratio A : B : C is (k/2) : (k/3) : (k/4). To clear the denominators, multiply by the LCM of 2, 3, and 4, which is 12. Ratio = 6 : 4 : 3.
254
Find the mean proportional between 9 and 25.
Answer:
15
The mean proportional between two numbers a and b is given by the square root of their product: sqrt(a * b). Here, mean proportional = sqrt(9 * 25) = sqrt(225) = 15.
255
The third proportional to 16 and 24 is:
Answer:
36
Let the third proportional be x. Then 16 : 24 :: 24 : x. Using the product of extremes and means, 16 * x = 24 * 24. 16x = 576. Solving for x gives x = 576 / 16 = 36.
256
The fourth proportional to 4, 9, 12 is:
Answer:
27
Let the fourth proportional be x. Then 4 : 9 :: 12 : x. In a proportion, the product of extremes equals the product of means. So, 4 * x = 9 * 12. 4x = 108, which gives x = 27.
257
Divide Rs. 1400 between A and B in the ratio 3 : 4. What is B's share?
Answer:
Rs. 800
The total number of parts in the ratio is 3 + 4 = 7 parts. The value of 1 part is 1400 / 7 = 200. Since B has 4 parts, B's share is 4 * 200 = Rs. 800.
258
If x : y = 3 : 4, find the value of (2x + 3y) : (3x - y).
Answer:
18 : 5
Let x = 3k and y = 4k. Substitute these values into the expression: (2(3k) + 3(4k)) / (3(3k) - 4k) = (6k + 12k) / (9k - 4k) = 18k / 5k. The k cancels out, leaving the ratio 18 : 5.
259
If A : B = 2 : 3 and B : C = 4 : 5, then what is the ratio of A : C?
Answer:
8 : 15
To find the combined ratio A : C, we can multiply the two ratios together. (A/B) * (B/C) = A/C. Therefore, (2/3) * (4/5) = 8/15. The ratio A : C is 8 : 15.