All Categories MCQs
Topic Notes: All Categories
General Description
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
7101
The age of A is 5/4 of B's age. The sum of their ages is 45. What is A's age?
Answer:
25
A = 5/4 B. A + B = 45 => 5/4 B + B = 45 => 9/4 B = 45 => B = 20. A = 25.
7102
Present ages of a father and a son are in the ratio 7:2. Five years ago, the product of their ages was 150. Find the present age of the father.
Answer:
35
Let ages be 7x and 2x. (7x - 5)(2x - 5) = 150. Try x=5: (35-5)*(10-5) = 30 * 5 = 150. Correct. Father = 35.
7103
If the ratio of present ages of A and B is 2 : 3 and 6 years ago the ratio was 1 : 2, what will be the ratio of their ages 6 years from now?
Answer:
3 : 4
Ages 2x, 3x. 6 years ago: (2x - 6)/(3x - 6) = 1/2 => 4x - 12 = 3x - 6 => x = 6. Present ages: 12, 18. After 6 years: 18, 24. Ratio = 18:24 = 3:4.
7104
The ratio of the ages of a man and his son is 4 : 1. If the product of their ages is 196, find the age of the man.
Answer:
28
Ages 4x and x. Product = 4x^2 = 196 => x^2 = 49 => x = 7. Man's age = 4x = 28.
7105
The product of the present ages of A and B is 750. If the ratio of their ages is 6 : 5, find the sum of their ages.
Answer:
55
Ages 6x and 5x. Product = 30x^2 = 750 => x^2 = 25 => x = 5. Sum of ages = 11x = 11 * 5 = 55.
7106
Raju is 5 years younger than his sister. His sister's age is 3 times the age of their brother. If their brother is 4 years old, what is Raju's age?
Answer:
7
Brother = 4. Sister = 3 * 4 = 12. Raju = Sister - 5 = 12 - 5 = 7.
7107
The sum of ages of A, B, C is 96 years. 10 years ago, the ratio of their ages was 1:2:3. What is the present age of B?
Answer:
32
Sum 10 years ago = 96 - 30 = 66. Ratio = 1:2:3. Total parts = 6. 6 parts = 66 => 1 part = 11. B's age 10 years ago = 2*11 = 22. Present age = 32.
7108
In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, what is the present age of A?
Answer:
48
A + 10 = 2(B - 10) => A + 10 = 2B - 20. Given A = B + 9. So B + 19 = 2B - 20 => B = 39. A = 39 + 9 = 48.
7109
10 years ago, the ratio of ages of A and B was 13 : 17. 17 years from now, the ratio will be 10 : 11. What is the present age of B?
Answer:
27
Let ages 10 years ago be 13x and 17x. Present: 13x+10, 17x+10. 17 yrs from now: 13x+27, 17x+27. Ratio: (13x+27)/(17x+27) = 10/11 => 143x + 297 = 170x + 270 => 27x = 27 => x = 1. Present age of B = 17(1) + 10 = 27.
7110
The difference between the ages of a mother and her daughter is 24 years. If the ratio of their ages is 5 : 1, what is the mother's age?
Answer:
30
Ratio 5x and x. Difference = 4x = 24 => x = 6. Mother's age = 5x = 30.