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
161
After 15 years, A will be 3 times as old as he was 5 years ago. What is his present age?
Answer:
15
A + 15 = 3(A - 5) => A + 15 = 3A - 15 => 2A = 30 => A = 15.
162
A father is 30 years older than his son. He will be three times as old as his son in 5 years. What is the son's present age?
Answer:
10
F = S + 30. F + 5 = 3(S + 5). Substitute F: S + 35 = 3S + 15 => 2S = 20 => S = 10.
163
The difference between the ages of A and B is 16 years. The ratio of their ages is 5 : 1. What is the sum of their ages?
Answer:
24
Difference = 4 parts = 16 => 1 part = 4. Sum = 6 parts = 6 * 4 = 24.
164
The ratio of the ages of A and B is 3:4. The sum of their ages is 28. What is the age of B after 5 years?
Answer:
21
Total parts = 7. 7 parts = 28 => 1 part = 4. B's present age = 4 * 4 = 16. After 5 years = 16 + 5 = 21.
165
A is 3 years older than B and 3 years younger than C. If the sum of their ages is 60, find the age of C.
Answer:
23
A = B + 3 => B = A - 3. A = C - 3 => C = A + 3. A + B + C = 60 => 3A = 60 => A = 20. C = 20 + 3 = 23.
166
Sum of the ages of A, B, and C is 90 years. 10 years ago, the ratio of their ages was 1 : 2 : 3. Find the present age of C.
Answer:
40
Sum 10 years ago = 90 - 30 = 60. Ratio 1:2:3. Total parts = 6. 1 part = 10. C's age 10 years ago = 3 * 10 = 30. Present age = 30 + 10 = 40.
167
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.
168
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.
169
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.
170
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.