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
151
An amount is to be distributed among A, B, and C in the ratio 3:1:5. The difference between B's and C's share is Rs. 3600. What is the total amount?
Answer:
Rs. 8100
Ratio is 3x, x, 5x. C - B = 5x - x = 4x. 4x = 3600 => x = 900. Total amount = 3x + x + 5x = 9x = 9 * 900 = Rs. 8100.
152
Three numbers are in the ratio 1:2:3 and the sum of their squares is 504. The numbers are:
Answer:
6, 12, 18
Let numbers be x, 2x, 3x. Sum of squares = x^2 + 4x^2 + 9x^2 = 14x^2 = 504. x^2 = 36 => x = 6. Numbers are 6, 12, 18.
153
If 20% of A = 30% of B = 1/6 of C, then A : B : C is:
Answer:
15:10:18
(1/5)A = (3/10)B = (1/6)C = k. A = 5k, B = 10k/3, C = 6k. Ratio A:B:C = 5 : 10/3 : 6. Multiply by 3 gives 15 : 10 : 18.
154
The compound ratio of 2:3, 5:4, and 3:7 is:
Answer:
5:14
Compound ratio = (2/3) * (5/4) * (3/7) = (2 * 5 * 3) / (3 * 4 * 7) = 30 / 84 = 5 / 14.
155
The ratio of boys to girls in a class is 4:5. If there are 20 boys, how many girls are there?
Answer:
25
Let the number of boys be 4x. 4x = 20 => x = 5. Number of girls is 5x = 5 * 5 = 25.
156
A sum of money is divided among A, B and C in the ratio 2:3:5. If A gets Rs. 100, then the total sum is:
Answer:
Rs. 500
A's share is 2 parts. 2 parts = 100 => 1 part = 50. Total parts = 2+3+5 = 10. Total sum = 10 * 50 = Rs. 500.
157
In a 729 liters mixture of milk and water, the ratio of milk to water is 7:2. To get a new mixture containing milk and water in the ratio 7:3, the amount of water to be added is:
Answer:
81 liters
Initial Milk = (7/9)*729 = 567 L. Initial Water = (2/9)*729 = 162 L. New ratio 7:3 implies water should be (3/7)*Milk = (3/7)*567 = 243 L. Amount to add = 243 - 162 = 81 liters.
158
A bag contains 50 P, 25 P and 10 P coins in the ratio 5: 9: 4, amounting to Rs. 206. Find the number of 50 P coins.
Answer:
200
Value in paise: 50(5x) + 25(9x) + 10(4x) = 250x + 225x + 40x = 515x. 515x = 20600 paise => x = 40. Number of 50 P coins = 5x = 200.
159
If 5A = 7B = 9C, then A : B : C is:
Answer:
63 : 45 : 35
A = k/5, B = k/7, C = k/9. Ratio = 1/5 : 1/7 : 1/9. Multiply by LCM(5,7,9) = 315. 315/5 : 315/7 : 315/9 = 63 : 45 : 35.
160
What number must be subtracted from each term of the ratio 17:33 so that it becomes 7:15?
Answer:
3
Let x be subtracted. (17 - x) / (33 - x) = 7 / 15. Cross-multiply: 15(17 - x) = 7(33 - x) => 255 - 15x = 231 - 7x => 8x = 24 => x = 3.