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.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Five children's ages are consecutive whole numbers and total 65 years. What is the middle child's age?
A. 13 years
B. 11 years
C. 15 years
D. 17 years
Correct Answer: A
For five consecutive numbers, the middle number equals the average. The average is 65/5 = 13.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Three ages are in geometric progression with common ratio 2 and total 42 years. What is the oldest age?
A. 21 years
B. 26 years
C. 29 years
D. 24 years
Correct Answer: D
Let the ages be x, 2x and 4x. Then 7x = 42, so x = 6 and the oldest age is 24.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Three ages are in the ratio 2:5:7. The oldest is 25 years older than the youngest. What is the middle age?
A. 22 years
B. 27 years
C. 25 years
D. 30 years
Correct Answer: C
The difference of 5 ratio parts equals 25, so one part is 5. The middle age is 5 × 5 = 25.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Four siblings' ages are in arithmetic progression with common difference 3 years. Their total age is 62 years. What is the oldest age?
A. 17 years
B. 20 years
C. 22 years
D. 25 years
Correct Answer: B
Let the ages be x, x + 3, x + 6 and x + 9. Then 4x + 18 = 62, so x = 11 and the oldest is 20.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of three siblings are consecutive even numbers and total 90 years. What is the oldest sibling's age?
A. 32 years
B. 28 years
C. 35 years
D. 38 years
Correct Answer: A
Let the ages be x, x + 2 and x + 4. Then 3x + 6 = 90, so x = 28 and the oldest is 32.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 7 members is 31 years. One member aged 43 leaves and two members aged 25 and 30 join. What is the new average age?
A. 28.25 years
B. 29 years
C. 29.5 years
D. 28.625 years
Correct Answer: D
Original total = 7 × 31 = 217. New total = 217 - 43 + 25 + 30 = 229 for 8 members. New average = 229/8 = 28.625.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 10 people is 25 years. Four of them have an average age of 20 years. What is the average age of the remaining six?
A. 27.5 years
B. 28 years
C. 28⅓ years
D. 29 years
Correct Answer: C
Total age = 10 × 25 = 250. The four people total 80. The remaining six total 170, so their average is 170/6 = 28⅓ years.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 11 players is 23 years. When their 35-year-old coach joins, what is the new average age?
A. 21 years
B. 24 years
C. 26 years
D. 29 years
Correct Answer: B
Players' total = 11 × 23 = 253. Adding the coach gives 288 for 12 people. The new average is 24.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A group of 8 people has an average age of 21 years, while another group of 12 has an average age of 29 years. What is their combined average age?
A. 25.8 years
B. 24.8 years
C. 25 years
D. 26 years
Correct Answer: A
Combined total = 8 × 21 + 12 × 29 = 516. Total people = 20, so combined average = 516/20 = 25.8.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 9 people is 40 years. Three people with an average age of 50 years leave. What is the average age of the remaining six?
A. 31 years
B. 38 years
C. 41 years
D. 35 years
Correct Answer: D
Original total = 9 × 40 = 360. The three leaving people total 150. Remaining total = 210, and 210/6 = 35.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of six family members is 26 years. What was their average age two years ago, assuming the same members?
A. 21 years
B. 26 years
C. 24 years
D. 29 years
Correct Answer: C
Two years ago every member was 2 years younger, so the average was 26 - 2 = 24.