CSS - PMS - CCE - PCS - Mathematics
Age Problems
Six years ago, the product of the ages of A and B was 180, and their age difference was 3 years. What is the older person's present age?
A. 21 years
B. 18 years
C. 23 years
D. 26 years
Correct Answer: A
Six years ago the factor pair of 180 differing by 3 was 12 and 15. Their present ages are 18 and 21, so the older person is 21.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother's two-digit age is the reverse of her daughter's age. Their ages total 77 years and differ by 27 years. What is the mother's age?
A. 48 years
B. 55 years
C. 58 years
D. 52 years
Correct Answer: D
The two ages are (77 + 27)/2 = 52 and (77 - 27)/2 = 25. They are digit reversals, so the mother is 52.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father's two-digit age is the reverse of his son's age. Their ages total 99 years and differ by 45 years. What is the father's age?
A. 66 years
B. 76 years
C. 72 years
D. 80 years
Correct Answer: C
Two numbers with sum 99 and difference 45 are 72 and 27. They are digit reversals, so the father's age is 72.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The older person is 7 years older than the younger person, and their age product is 330. What is the younger person's age?
A. 12 years
B. 15 years
C. 17 years
D. 20 years
Correct Answer: B
Let the younger age be x. Then x(x + 7) = 330, so x² + 7x - 330 = 0. Factoring gives (x - 15)(x + 22) = 0, so x = 15.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of two ages is 32 years and their product is 255. What is the older age?
A. 17 years
B. 14 years
C. 19 years
D. 22 years
Correct Answer: A
The two numbers with sum 32 and product 255 are 15 and 17. Hence the older age is 17.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The product of two ages is 432 and their difference is 6 years. What is the older age?
A. 21 years
B. 26 years
C. 29 years
D. 24 years
Correct Answer: D
The factor pair of 432 differing by 6 is 18 and 24. Therefore the older age is 24.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother was 24 years old when her daughter was born. If the daughter is 17 years old in 2026, what is the mother's age?
A. 37 years
B. 44 years
C. 41 years
D. 47 years
Correct Answer: C
The mother is always 24 years older than the daughter. Therefore her age is 17 + 24 = 41.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father was born in 1982 and his son in 2010. In which year will the father be exactly twice the son's age?
A. 2036
B. 2038
C. 2040
D. 2042
Correct Answer: B
Let the year be y. Then y - 1982 = 2(y - 2010). Solving gives y = 2038.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The combined age of two people is 74 years in 2026. In which year will their combined age become 94 years?
A. 2036
B. 2034
C. 2035
D. 2037
Correct Answer: A
Their combined age increases by 2 each year. An increase of 20 therefore takes 10 years, so the year will be 2026 + 10 = 2036.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A will be 36 years old in 2028. How old was A in 2015?
A. 20 years
B. 25 years
C. 28 years
D. 23 years
Correct Answer: D
The time from 2015 to 2028 is 13 years. Therefore A's age in 2015 was 36 - 13 = 23.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A person was born in 1998. How old will the person be on 31 December 2026?
A. 25 years
B. 30 years
C. 28 years
D. 33 years
Correct Answer: C
By 31 December 2026, the full-year difference is 2026 - 1998 = 28 years.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father and his three sons have ages in the ratio 9:4:3:2 and total 72 years. What is the youngest son's age?
A. 6 years
B. 8 years
C. 10 years
D. 12 years
Correct Answer: B
The ratio parts total 18, so one part is 72/18 = 4. The youngest son's age is 2 × 4 = 8.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Twin brothers are each 14 years old. Their combined age with their sister is 47 years. What is the sister's age?
A. 19 years
B. 16 years
C. 21 years
D. 24 years
Correct Answer: A
The twins total 28 years. The sister's age is 47 - 28 = 19.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Three ages are in the ratio of the consecutive odd numbers 3:5:7 and total 90 years. What is the middle age?
A. 26 years
B. 33 years
C. 36 years
D. 30 years
Correct Answer: D
The ratio parts total 15. One part is 90/15 = 6, so the middle age is 5 × 6 = 30.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of four people are x, x + 2, x + 6 and x + 12. If their average age is 24 years, what is the oldest age?
A. 27 years
B. 34 years
C. 31 years
D. 37 years
Correct Answer: C
Their total is 96. So 4x + 20 = 96, giving x = 19. The oldest age is x + 12 = 31.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Three siblings' ages are in the ratio 3:4:6. The eldest is 15 years older than the youngest. What is their total age?
A. 59 years
B. 65 years
C. 69 years
D. 73 years
Correct Answer: B
The difference of 3 ratio parts equals 15, so one part is 5. Their ages are 15, 20 and 30, totaling 65.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Four ages are in arithmetic progression. The youngest is 16 years and the oldest is 28 years. What is the second-youngest age?
A. 20 years
B. 17 years
C. 22 years
D. 25 years
Correct Answer: A
The total span is 12 over three equal intervals, so the common difference is 4. The ages are 16, 20, 24 and 28.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of four generations are in the ratio 1:2:4:7 and total 98 years. What is the oldest person's age?
A. 45 years
B. 52 years
C. 55 years
D. 49 years
Correct Answer: D
The ratio parts total 14. One part is 98/14 = 7, so the oldest age is 7 × 7 = 49.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of three people is 26 years. The eldest is 8 years older than the middle person, who is 5 years older than the youngest. What is the eldest age?
A. 29 years
B. 36 years
C. 33 years
D. 39 years
Correct Answer: C
Let the youngest be x. Then the ages are x, x + 5 and x + 13. Their total is 78, so 3x + 18 = 78 and x = 20. The eldest is 33.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
For three people A, B and C: A + B = 52, B + C = 60 and A + C = 56. What is B's age?
A. 25 years
B. 28 years
C. 30 years
D. 33 years
Correct Answer: B
Adding the first two equations and subtracting the third gives 2B = 56, so B = 28.