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The MCQs below are drawn from the Mathematics subject category.
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7181
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.
7182
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.
7183
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.
7184
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.
7185
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.
7186
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.
7187
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.
7188
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.
7189
A is 2 years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?
Let C's age be x. Then B's age is 2x, and A's age is 2x + 2. Total age = x + 2x + (2x + 2) = 27. 5x + 2 = 27 => 5x = 25 => x = 5. B's age is 2x = 2 * 5 = 10 years.
7190
The ratio of the present ages of two brothers is 1 : 2. 5 years back, the ratio was 1 : 3. What will be the ratio of their ages after 5 years?
Let present ages be x and 2x. 5 years ago: (x - 5) / (2x - 5) = 1 / 3. Cross-multiplying: 3x - 15 = 2x - 5 => x = 10. Present ages are 10 and 20. After 5 years, ages will be 15 and 25. Ratio is 15 : 25 = 3 : 5.
