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
231
A father said to his son, 'I was as old as you are at the present at the time of your birth.' If the father's age is 38 years now, the son's age five years back was:
Answer:
14 years
Let son's present age be S. Father's age at son's birth was 38 - S. Given that 38 - S = S => 2S = 38 => S = 19. Son's age 5 years back = 19 - 5 = 14 years.
232
The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is:
Answer:
35 years
Let ages be x and x - 10. 15 years ago: (x - 15) = 2(x - 10 - 15) => x - 15 = 2(x - 25) => x - 15 = 2x - 50 => x = 35. Elder person is 35 years old.
233
The ratio between the school ages of Neelam and Shaan is 5 : 6 respectively. If the ratio between the one-third age of Neelam and half of Shaan's age is 5 : 9, then what is the school age of Shaan?
Answer:
Cannot be determined
Let Neelam's age be 5x and Shaan's be 6x. Condition: (1/3 of 5x) / (1/2 of 6x) = 5/9 => (5x/3) / 3x = 5/9 => 5/9 = 5/9. This is an identity and gives no new information to solve for x. Hence, x cannot be determined.
234
The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
Answer:
4 years
Let the ages be x, x+3, x+6, x+9, x+12. Sum = 5x + 30 = 50 => 5x = 20 => x = 4. The youngest child is 4 years old.
235
Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?
Answer:
2 times
Three times MORE means Father = S + 3S = 4S. After 8 years: 4S + 8 = 2.5(S + 8) => 4S + 8 = 2.5S + 20 => 1.5S = 12 => S = 8. Father's present age = 32. After further 8 years (16 years from now), Son = 8 + 16 = 24, Father = 32 + 16 = 48. Ratio = 48 / 24 = 2 times.
236
Ten years ago, A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages?
Answer:
35
Present ages are 3x and 4x. Ten years ago: 3x - 10 = (1/2)(4x - 10) => 6x - 20 = 4x - 10 => 2x = 10 => x = 5. Present ages are 15 and 20. Total = 15 + 20 = 35.
237
The ratio of the ages of a man and his wife is 4 : 3. After 4 years, this ratio will be 9 : 7. If at the time of marriage, the ratio was 5 : 3, then how many years ago were they married?
Answer:
12 years
Present ages 4x and 3x. After 4 years: (4x + 4) / (3x + 4) = 9 / 7 => 28x + 28 = 27x + 36 => x = 8. Present ages are 32 and 24. Let them be married y years ago. (32 - y) / (24 - y) = 5 / 3 => 96 - 3y = 120 - 5y => 2y = 24 => y = 12 years.
238
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
Answer:
12
Given: (A + B) = (B + C) + 12. Subtracting B from both sides gives A = C + 12. This means A is 12 years older than C, so C is 12 years younger than A.
239
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Answer:
7 : 3
Let present ages be F and S. F - 10 = 3(S - 10) => F - 3S = -20. Also, F + 10 = 2(S + 10) => F - 2S = 10. Subtracting the first from the second: S = 30. Then F = 70. Ratio = 70 : 30 = 7 : 3.
240
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
Answer:
40 years
Let the mother's present age be M. Person's age = (2/5)M. After 8 years: (2/5)M + 8 = (1/2)(M + 8). Multiplying by 10: 4M + 80 = 5M + 40 => M = 40. The mother is 40 years old.