CSS - PMS - CCE - PCS - Mathematics
Age Problems
Three years from now, the ages of A and B will be in the ratio 7:9. Nine years ago, their ages were in the ratio 2:3. What is A's present age?
A. 25 years
B. 22 years
C. 27 years
D. 30 years
Correct Answer: A
Three years from now let the ages be 7x and 9x. Nine years ago they were 7x - 12 and 9x - 12. Their ratio 2:3 gives x = 4. Thus A's present age is 28 - 3 = 25.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Nine years ago, the ages of A and B were in the ratio 4:7. If their present ages total 62 years, what is A's present age?
A. 22 years
B. 27 years
C. 30 years
D. 25 years
Correct Answer: D
Nine years ago let the ages be 4x and 7x. Present total is 11x + 18 = 62, so x = 4. A's present age is 4x + 9 = 25.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 8:5. Ten years from now, their ages will be in the ratio 10:7. What is B's present age?
A. 22 years
B. 27 years
C. 25 years
D. 30 years
Correct Answer: C
Let present ages be 8x and 5x. Then (8x + 10)/(5x + 10) = 10/7. Solving gives x = 5, so B = 25.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 3:7, and their age difference is 16 years. What will their age ratio be after 12 years?
A. 2:3
B. 3:5
C. 4:7
D. 5:8
Correct Answer: B
The difference of 4 ratio parts equals 16, so one part is 4. Present ages are 12 and 28. After 12 years they are 24 and 40, whose ratio is 3:5.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A is 12 years older than B. Six years ago, their ages were in the ratio 5:3. What is A's present age?
A. 36 years
B. 32 years
C. 39 years
D. 42 years
Correct Answer: A
Let B's present age be x, so A is x + 12. Six years ago, (x + 6)/(x - 6) = 5/3. Solving gives x = 24, so A = 36.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Four years ago, the ages of A and B were in the ratio 5:9. Eight years from now, their ages will be in the ratio 9:13. What is B's present age?
A. 27 years
B. 34 years
C. 37 years
D. 31 years
Correct Answer: D
Four years ago let the ages be 5x and 9x. Eight years from now they are 5x + 12 and 9x + 12. Their ratio is 9:13, giving x = 3. Thus B's present age is 9x + 4 = 31.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Seven years from now, the ages of A and B will be in the ratio 5:7. Their present ages total 46 years. What is A's present age?
A. 15 years
B. 20 years
C. 18 years
D. 23 years
Correct Answer: C
Seven years from now the total will be 46 + 14 = 60. The ratio parts total 12, so one part is 5. A's future age is 25 and present age is 25 - 7 = 18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Five years ago, the ages of A and B were in the ratio 2:5. Their present age difference is 21 years. What is B's present age?
A. 36 years
B. 40 years
C. 43 years
D. 46 years
Correct Answer: B
Five years ago let the ages be 2x and 5x. The difference is always 3x, so 3x = 21 and x = 7. B's present age is 5x + 5 = 40.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 7:11. After 8 years, their ages will be in the ratio 9:13. What is their present total age?
A. 72 years
B. 66 years
C. 76 years
D. 80 years
Correct Answer: A
Let present ages be 7x and 11x. Then (7x + 8)/(11x + 8) = 9/13. Solving gives x = 4. Their total is 18x = 72.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are 25 and 40 years respectively. What was their age ratio five years ago?
A. 3:5
B. 5:8
C. 4:9
D. 4:7
Correct Answer: D
Five years ago, their ages were 20 and 35. The ratio 20:35 simplifies to 4:7.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 4:7. After 8 years, the ratio will be 2:3. What is A's present age?
A. 13 years
B. 18 years
C. 16 years
D. 21 years
Correct Answer: C
Let the ages be 4x and 7x. Then (4x + 8)/(7x + 8) = 2/3. Thus 12x + 24 = 14x + 16, so x = 4 and A = 16.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Four years from now, a person's age will be 20% greater than the present age. What is the present age?
A. 17 years
B. 20 years
C. 22 years
D. 25 years
Correct Answer: B
Let present age be x. Then x + 4 = 1.20x. Therefore 0.20x = 4 and x = 20.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A person's age nine years from now will be three years more than twice the age six years ago. What is the present age?
A. 18 years
B. 15 years
C. 20 years
D. 23 years
Correct Answer: A
Let present age be x. Then x + 9 = 2(x - 6) + 3. Hence x + 9 = 2x - 9, so x = 18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Eighteen years from now, a person's age will be three times the age six years ago. What is the present age?
A. 15 years
B. 20 years
C. 23 years
D. 18 years
Correct Answer: D
Let present age be x. Then x + 18 = 3(x - 6). Thus x + 18 = 3x - 18, so x = 18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ratio of a person's age ten years ago to the age fourteen years from now is 2:5. What is the present age?
A. 23 years
B. 28 years
C. 26 years
D. 31 years
Correct Answer: C
Let present age be x. Then (x - 10)/(x + 14) = 2/5. So 5x - 50 = 2x + 28, giving x = 26.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Five years ago, a person's age was three-fourths of the age seven years from now. What is the present age?
A. 37 years
B. 41 years
C. 44 years
D. 47 years
Correct Answer: B
Let present age be x. Then x - 5 = (3/4)(x + 7). Thus 4x - 20 = 3x + 21, giving x = 41.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Fifteen years from now, a person's age will be seven-fourths of the present age. What is the present age?
A. 20 years
B. 17 years
C. 22 years
D. 25 years
Correct Answer: A
Let present age be x. Then x + 15 = 7x/4. Hence 4x + 60 = 7x, so x = 20.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ratio of a person's age four years ago to the age eight years from now is 3:5. What is the present age?
A. 19 years
B. 24 years
C. 27 years
D. 22 years
Correct Answer: D
Let the present age be x. Then (x - 4)/(x + 8) = 3/5. Thus 5x - 20 = 3x + 24, so x = 22.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Twelve years from now, a person's age will be five-thirds of the age six years ago. What is the present age?
A. 29 years
B. 36 years
C. 33 years
D. 39 years
Correct Answer: C
Let the present age be x. Then x + 12 = (5/3)(x - 6). Multiplying by 3 gives 3x + 36 = 5x - 30, so x = 33.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Eight years ago, a person's age was 60% of the present age. What is the present age?
A. 17 years
B. 20 years
C. 22 years
D. 25 years
Correct Answer: B
Let the present age be x. Then x - 8 = 0.60x. Hence 0.40x = 8 and x = 20.