CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother is four times as old as her daughter. Twelve years ago, she was ten times as old. What is the mother's present age?
A. 72 years
B. 66 years
C. 76 years
D. 80 years
Correct Answer: A
Let the daughter's age be x and the mother's age be 4x. Then 4x - 12 = 10(x - 12). Solving gives x = 18, so the mother is 72.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father is 32 years older than his son. After 8 years, the father will be twice as old as the son. What is the father's present age?
A. 52 years
B. 59 years
C. 62 years
D. 56 years
Correct Answer: D
Let the son's age be x, so the father is x + 32. After 8 years, x + 40 = 2(x + 8). Thus x = 24 and the father is 56.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The older person's age is 150% of the younger person's age, and their difference is 18 years. What is the older person's age?
A. 50 years
B. 57 years
C. 54 years
D. 60 years
Correct Answer: C
Let the younger age be x. The older age is 1.5x. Their difference is 0.5x = 18, so x = 36 and the older age is 54.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of two ages is 61 years. The older person is 7 years more than twice the younger person. What is the younger person's age?
A. 15 years
B. 18 years
C. 20 years
D. 23 years
Correct Answer: B
Let the younger age be x. The older age is 2x + 7. Then 3x + 7 = 61, so x = 18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Two ages are in the ratio 9:5 and their product is 1125. What is the sum of their ages?
A. 70 years
B. 64 years
C. 74 years
D. 78 years
Correct Answer: A
Let the ages be 9x and 5x. Their product is 45x² = 1125, so x² = 25 and x = 5. The ages are 45 and 25, totaling 70.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of two present ages is 96 years and their age difference is 18 years. What is the older person's age?
A. 53 years
B. 60 years
C. 63 years
D. 57 years
Correct Answer: D
Let the older and younger ages be O and Y. Then O + Y = 96 and O - Y = 18. Adding gives 2O = 114, so O = 57.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A is 25% younger than B, and their ages total 63 years. What is A's age?
A. 24 years
B. 29 years
C. 27 years
D. 32 years
Correct Answer: C
A is 75% of B. Let B = x, so A = 0.75x. Then 1.75x = 63, giving B = 36 and A = 27.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A's age is two-thirds of B's present age. Six years ago, A's age was half of B's age. What is their present total age?
A. 26 years
B. 30 years
C. 33 years
D. 36 years
Correct Answer: B
Let B's age be x and A's age be 2x/3. Then 2x/3 - 6 = (x - 6)/2. Solving gives x = 18 and A = 12, so their total is 30.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of two ages is 56 years and their difference is 20 years. What is the younger person's age?
A. 18 years
B. 15 years
C. 20 years
D. 23 years
Correct Answer: A
Let the older and younger ages be O and Y. Then O + Y = 56 and O - Y = 20. Subtracting gives 2Y = 36, so Y = 18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of two people is 31 years and their age difference is 8 years. What is the older person's age?
A. 31 years
B. 38 years
C. 41 years
D. 35 years
Correct Answer: D
Their total age is 62. If the older age is O and younger age is Y, then O + Y = 62 and O - Y = 8. Hence 2O = 70 and O = 35.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of two ages is 84 years, and the younger age is five-sevenths of the older age. What is the older age?
A. 45 years
B. 52 years
C. 49 years
D. 55 years
Correct Answer: C
Let the ages be 5x and 7x. Then 12x = 84, so x = 7 and the older age is 49.
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.