CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father was 29 years old when his son was born. At present, the father is 9 years more than twice the son's age. What is the son's present age?
A. 17 years
B. 20 years
C. 22 years
D. 25 years
Correct Answer: B
The age difference is always 29, so father = son + 29. Also father = 2(son) + 9. Hence son + 29 = 2son + 9, giving son = 20.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A grandmother is 24 years older than the mother, and the mother is 22 years older than the daughter. Their total age is 119 years. What is the mother's age?
A. 39 years
B. 35 years
C. 42 years
D. 45 years
Correct Answer: A
Let the daughter's age be x. Then mother = x + 22 and grandmother = x + 46. So 3x + 68 = 119, giving x = 17 and mother = 39.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother is twice the combined age of her two children. Their total family age is 78 years, and the children's ages are in the ratio 5:8. What is the elder child's age?
A. 13 years
B. 18 years
C. 21 years
D. 16 years
Correct Answer: D
Let the children's combined age be S. Then mother = 2S and 3S = 78, so S = 26. Dividing 26 in the ratio 5:8 gives ages 10 and 16.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father and his two daughters have a total age of 92 years. The father is 12 years older than the daughters' combined age. The daughters differ by 4 years. What is the younger daughter's age?
A. 15 years
B. 20 years
C. 18 years
D. 23 years
Correct Answer: C
Let the daughters' combined age be S. Then father = S + 12 and 2S + 12 = 92, so S = 40. Two ages totaling 40 and differing by 4 are 18 and 22.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother is 26 years older than her son. After 7 years, their combined age will be 72 years. What is the mother's present age?
A. 38 years
B. 42 years
C. 45 years
D. 48 years
Correct Answer: B
Their present combined age is 72 - 14 = 58. Let the son's age be x and mother's age be x + 26. Then 2x + 26 = 58, so x = 16 and mother = 42.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of a grandfather, father and son are in the ratio 8:5:2. The grandfather is 36 years older than the son. What is the father's age?
A. 30 years
B. 26 years
C. 33 years
D. 36 years
Correct Answer: A
The difference between grandfather and son is 6 ratio parts. So 6 parts = 36 and one part = 6. The father's age is 5 × 6 = 30.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father is three times as old as his son. After 4 years, he will be two-and-a-half times as old. What is the father's present age?
A. 32 years
B. 39 years
C. 42 years
D. 36 years
Correct Answer: D
Let the son's age be x and father's age be 3x. Then 3x + 4 = 2.5(x + 4). Solving gives x = 12, so the father is 36.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother and daughter have a total age of 54 years. Six years from now, the mother will be twice as old as the daughter. What is the daughter's present age?
A. 13 years
B. 18 years
C. 16 years
D. 21 years
Correct Answer: C
Let the daughter's age be x and mother's age be 54 - x. Then 60 - x = 2(x + 6). Solving gives x = 16.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of a father and son total 82 years. Six years ago, the father was four times as old as the son. What is the father's present age?
A. 56 years
B. 62 years
C. 66 years
D. 70 years
Correct Answer: B
Let the son's age be x, so the father's age is 82 - x. Six years ago, 76 - x = 4(x - 6). Solving gives x = 20 and father = 62.
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.