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
181
The ages of A and B are in the ratio 6 : 5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?
Answer:
8 : 7
Total parts = 11. 11 parts = 44 => 1 part = 4. Ages are 24 and 20. After 8 years: 32 and 28. Ratio = 32 : 28 = 8 : 7.
182
If the sum of the ages of A and B is 60 and the ratio of their ages is 2 : 3, what is the age of A?
Answer:
24
Total parts = 5. 5 parts = 60 => 1 part = 12. A = 2 parts = 24.
183
A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?
Answer:
45
M = 2S. 20 years ago: M - 20 = 10(S - 20). Substitute M: 2S - 20 = 10S - 200 => 8S = 180 => S = 22.5. Mother = 45.
184
Ravi is 15 years younger than his brother. After 5 years, the ratio of their ages will be 2 : 3. What is Ravi's present age?
Answer:
25
Let brother be x. Ravi is x - 15. After 5 years: Ravi = x - 10, Brother = x + 5. (x - 10) / (x + 5) = 2 / 3 => 3x - 30 = 2x + 10 => x = 40. Ravi = 40 - 15 = 25.
185
The present age of a boy is one-third of his father's age. 15 years hence, he will be half of his father's age. The present age of the boy is:
Answer:
15
B = F/3 => F = 3B. In 15 years: B + 15 = (F + 15)/2. Substitute F: 2(B + 15) = 3B + 15 => 2B + 30 = 3B + 15 => B = 15.
186
The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.
Answer:
30, 40
Ages 3x, 4x. (3x - 5)/(4x - 5) = 5/7 => 21x - 35 = 20x - 25 => x = 10. Present ages are 30 and 40.
187
A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is:
Answer:
22
M = S + 24. In 2 years: M + 2 = 2(S + 2). Substitute M: (S + 24) + 2 = 2S + 4 => S + 26 = 2S + 4 => S = 22.
188
The ratio of the ages of Swati and Varun is 2 : 5. After 8 years, their ages will be in the ratio 1 : 2. What is the sum of their present ages?
Answer:
56
Ages 2x, 5x. (2x+8)/(5x+8) = 1/2 => 4x+16 = 5x+8 => x = 8. Sum = 7x = 7 * 8 = 56.
189
The total of the ages of Jayant, Prem and Saransh is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Saransh?
Answer:
38
Sum of ages 10 years ago = 93 - 3(10) = 63. Ratio was 2:3:4 (sum=9 parts). 9 parts = 63 => 1 part = 7. Saransh's age 10 years ago = 4 * 7 = 28. Present age = 28 + 10 = 38.
190
Ten years ago, P was half of Q in age. If the ratio of their present ages is 3 : 4, what is Q's present age?
Answer:
20
Present ages 3x and 4x. 10 years ago: 3x - 10 = (1/2)(4x - 10) => 6x - 20 = 4x - 10 => 2x = 10 => x = 5. Q's present age = 4x = 20.