CSS - PMS - CCE - PCS - Mathematics
Age Problems
A is 8 years less than one-and-a-half times B's age. Their ages total 52 years. What is A's age?
A. 25 years
B. 28 years
C. 30 years
D. 33 years
Correct Answer: B
Let B's age be x. Then A = 1.5x - 8. So 2.5x - 8 = 52, giving x = 24 and A = 28.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
One person's age is 40% greater than another's. Their total age is 60 years. What is the older person's age?
A. 35 years
B. 31 years
C. 38 years
D. 41 years
Correct Answer: A
Let the younger age be x. The older age is 1.4x. Then 2.4x = 60, so x = 25 and the older age is 35.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The younger person is four-sevenths as old as the older person, and their age difference is 18 years. What is the older person's age?
A. 38 years
B. 45 years
C. 48 years
D. 42 years
Correct Answer: D
Let the older age be 7x and younger age be 4x. Their difference is 3x = 18, so x = 6 and the older age is 42.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of the present ages of A and B is 66 years. A is 6 years less than twice B's age. What is A's age?
A. 38 years
B. 45 years
C. 42 years
D. 48 years
Correct Answer: C
Let B's age be x. Then A = 2x - 6 and 3x - 6 = 66. Thus x = 24 and A = 42.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A's present age is 75% of B's age. After 6 years, A's age will be 80% of B's age. What is A's present age?
A. 15 years
B. 18 years
C. 20 years
D. 23 years
Correct Answer: B
Let B's age be x, so A is 0.75x. Then 0.75x + 6 = 0.80(x + 6). Solving gives x = 24 and A = 18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 2:5. After 15 years, their ages will be in the ratio 5:8. What is their present total age?
A. 35 years
B. 31 years
C. 38 years
D. 41 years
Correct Answer: A
Let present ages be 2x and 5x. Then (2x + 15)/(5x + 15) = 5/8. Solving gives x = 5. Their total is 7x = 35.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Ten years ago, the ages of A and B were in the ratio 3:8. Their present ages are in the ratio 1:2. What is B's present age?
A. 46 years
B. 53 years
C. 56 years
D. 50 years
Correct Answer: D
Ten years ago let ages be 3x and 8x. Present ages are 3x + 10 and 8x + 10. Their ratio is 1:2, so x = 5. Hence B = 50.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 11:13. Six years ago, their ages were in the ratio 5:6. What is A's present age?
A. 60 years
B. 70 years
C. 66 years
D. 74 years
Correct Answer: C
Let present ages be 11x and 13x. Then (11x - 6)/(13x - 6) = 5/6. Solving gives x = 6, so A = 66.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of two people are in the ratio 3:5 and differ by 10 years. After how many years will their age ratio become 5:7?
A. 8 years
B. 10 years
C. 12 years
D. 14 years
Correct Answer: B
The present ages are 15 and 25 because 2 parts equal 10. Let the required time be t. Then (15 + t)/(25 + t) = 5/7, giving t = 10.
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.