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.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of five workers is 34 years. A 42-year-old worker is replaced and the new average becomes 32 years. What is the replacement's age?
A. 28 years
B. 32 years
C. 35 years
D. 38 years
Correct Answer: B
Original total = 5 × 34 = 170. New total = 5 × 32 = 160. The replacement's age is 160 - (170 - 42) = 32.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 24 students is 15 years. Fourteen boys have an average age of 16 years. What is the average age of the 10 girls?
A. 13.6 years
B. 13.2 years
C. 14 years
D. 14.4 years
Correct Answer: A
Total age = 24 × 15 = 360. Boys' total = 14 × 16 = 224. Girls' total = 136, so their average is 136/10 = 13.6.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of four brothers is 20 years. Their 10-year-old sister joins the group. What is the new average age?
A. 15 years
B. 20 years
C. 23 years
D. 18 years
Correct Answer: D
The brothers' total age is 4 × 20 = 80. Adding the sister gives 90 for five children, so the new average is 18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 14 students is 17 years. When their teacher joins, the average becomes 18 years. What is the teacher's age?
A. 28 years
B. 35 years
C. 32 years
D. 38 years
Correct Answer: C
Students' total = 14 × 17 = 238. Total including teacher = 15 × 18 = 270. Teacher's age = 32.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 8 team members is 26 years. Two members whose ages total 44 leave, and two members whose ages total 60 join. What is the new average?
A. 25 years
B. 28 years
C. 30 years
D. 33 years
Correct Answer: B
Original total = 8 × 26 = 208. New total = 208 - 44 + 60 = 224. Dividing by 8 gives an average of 28.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of a husband, wife and child is 28 years. The average age of the husband and wife is 39 years. What is the child's age?
A. 6 years
B. 4 years
C. 8 years
D. 10 years
Correct Answer: A
Family total = 3 × 28 = 84. Husband and wife total = 2 × 39 = 78. Child's age = 84 - 78 = 6.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of six people is 22 years. The ages of five of them total 100 years. What is the sixth person's age?
A. 28 years
B. 35 years
C. 38 years
D. 32 years
Correct Answer: D
The total age of six people is 6 × 22 = 132. The sixth person's age is 132 - 100 = 32.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 9 workers is 27 years. A 35-year-old worker joins them. What is the new average age?
A. 27.5 years
B. 28 years
C. 27.8 years
D. 28.5 years
Correct Answer: C
Original total = 9 × 27 = 243. New total = 243 + 35 = 278 for 10 workers. New average = 27.8.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of five family members is 32 years. What will their average age be after 4 years if no one joins or leaves?
A. 32 years
B. 36 years
C. 39 years
D. 42 years
Correct Answer: B
Every member becomes 4 years older, so the average also increases by 4: 32 + 4 = 36.