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The MCQs below are drawn from the Mathematics subject category.
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7171
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?
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.
7173
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:
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.
7174
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?
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.
7175
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
When Ayesha was born, father was 38. Her brother was born 4 years later. At that time, her father was 38 + 4 = 42 years old. Her mother was 36 years old when the brother was born. Difference = 42 - 36 = 6 years.
7176
The present ages of A, B and C are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
Let present ages be 4x, 7x, and 9x. Eight years ago, their sum was 56. So, (4x - 8) + (7x - 8) + (9x - 8) = 56 => 20x - 24 = 56 => 20x = 80 => x = 4. Present ages are 16, 28, and 36 years.
7177
At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun's age will be 26 years. What is the age of Deepak at present?
Let present ages be 4x and 3x. Arun's age after 6 years: 4x + 6 = 26 => 4x = 20 => x = 5. Deepak's present age = 3x = 3 * 5 = 15 years.
7178
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:
Let present ages be F and S. F + S = 60. Six years ago: F - 6 = 5(S - 6) => F - 5S = -24. Substitute F = 60 - S: 60 - S - 5S = -24 => 6S = 84 => S = 14. Son's age after 6 years = 14 + 6 = 20 years.
7179
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
Let their ages 6 years ago be 6x and 5x. Present ages: 6x + 6 and 5x + 6. Four years hence: (6x + 10) / (5x + 10) = 11 / 10. 60x + 100 = 55x + 110 => 5x = 10 => x = 2. Sagar's present age is 5x + 6 = 5(2) + 6 = 16 years.
7180
Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years?
Let present ages be 5x and 4x. Three years hence: (5x + 3) / (4x + 3) = 11 / 9. Cross-multiplying: 45x + 27 = 44x + 33 => x = 6. Anand's present age is 4x = 4 * 6 = 24 years.
