Let the son's age be s. The father's age is s+24. In two years, the son will be s+2 and the father will be s+26. Setting up the equation s+26 = 2(s+2) leads to s+26 = 2s+4, which simplifies to s = 22.
32
A is 4 years younger than B. If the ratio of their ages is 7:10, determine the current age of A.
Let A's age be 7x and B's age be 10x. The difference is 10x - 7x = 3x. We are given the difference is 4 years, so 3x = 4, which means x = 4/3. A's age is 7 * (4/3) = 28/3, which is approximately 9.33 years. Since 9.33 is not among the provided options, 'None of these' is the correct choice.
33
The sum of the ages of A and B is 36 years, and the difference between their ages is 6 years. What are their respective ages?
Let the ages be x and y. We have x + y = 36 and x - y = 6. Adding the equations gives 2x = 42, so x = 21. Substituting x back gives 21 + y = 36, so y = 15. The ages are 21 and 15. The provided answer choice B represents these values.
34
A father's current age is three times that of his son. In 15 years, the father's age will be double his son's age. What is the son's current age?
Let the son's current age be x. The father's age is 3x. In 15 years, the son will be x+15 and the father will be 3x+15. According to the problem, 3x+15 = 2(x+15). Solving this equation, 3x+15 = 2x+30, which simplifies to x = 15. Thus, the son is currently 15 years old.
35
Six years ago, the ratio of Khalid's age to Sadaf's age was 6:5. Four years from now, the ratio will be 11:10. Determine Sadaf's current age.
Let their ages six years ago be 6x and 5x. Their current ages are 6x+6 and 5x+6. Four years later, they will be 6x+10 and 5x+10. Setting (6x+10)/(5x+10) = 11/10 and solving for x gives x=2. Sadaf's current age is 5(2)+6 = 16.
36
A father is 24 years older than his son. In two years, the father's age will be double his son's age. What is the son's current age?
Let the son's current age be s. The father's age is s + 24. In two years, the son will be s + 2 and the father will be s + 26. Setting up the equation s + 26 = 2(s + 2) and solving for s yields 22 years.
37
If A's sister is 15 years old, A is 4 years older than his sister, and A is 6 years younger than his brother, while his mother is twice as old as his brother, what is the mother's age?
Given the sister is 15, A is 15 + 4 = 19. Since A is 6 years younger than his brother, the brother is 19 + 6 = 25. The mother is twice the brother's age, so 2 * 25 = 50. This calculation confirms the mother is 50 years old.
38
Rashid is positioned 15th from the front in a line of boys. The number of boys behind him is three times the number of boys in front of him. How many boys are located between Rashid and the boy who is 7th from the end of the line?
Rashid is 15th, meaning 14 boys are in front. There are 14 * 3 = 42 boys behind him. Total boys = 14 + 1 + 42 = 57. The 7th boy from the end is at position 57 - 7 + 1 = 51. The number of boys between position 15 and 51 is 51 - 15 - 1 = 35.
39
If 12 years are added to two-thirds of Rani's current age, the result is three years more than her present age. Determine Rani's current age.
Let A represent Rani's present age. The problem states that (2/3)A + 12 = A + 3. By rearranging the equation, we subtract (2/3)A from A to get (1/3)A, and subtract 3 from 12 to get 9. Therefore, (1/3)A = 9, which means A = 27 years.
40
A person's current age is two-fifths of his mother's age. In eight years, his age will be one-half of his mother's age. What is the mother's current age?
Let the mother's current age be M. The person's age is 0.4M. After 8 years, the person's age is 0.4M + 8 and the mother's age is M + 8. Setting up the equation 0.4M + 8 = 0.5(M + 8) leads to 0.4M + 8 = 0.5M + 4, which simplifies to 0.1M = 4, resulting in M = 40 years.
