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.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of a class including one teacher is 18 years. The average age of the 20 students alone is 16.5 years. What is the teacher's age?
A. 48 years
B. 44 years
C. 51 years
D. 54 years
Correct Answer: A
Total age including teacher = 21 × 18 = 378. Students' total = 20 × 16.5 = 330. Teacher's age = 48.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 20 boys is 14 years, and that of 30 girls is 16 years. What is the combined average age?
A. 14.8 years
B. 15 years
C. 15.5 years
D. 15.2 years
Correct Answer: D
Combined total = 20 × 14 + 30 × 16 = 760. Total students = 50. Combined average = 760/50 = 15.2.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 10 trainees decreases by 1.5 years when a 30-year-old trainee is replaced. What is the replacement's age?
A. 12 years
B. 17 years
C. 15 years
D. 20 years
Correct Answer: C
A decrease of 1.5 in the average of 10 means the total decreases by 15. The replacement is 30 - 15 = 15.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 8 people increases by 2 years when a 20-year-old person is replaced. What is the age of the new person?
A. 32 years
B. 36 years
C. 39 years
D. 42 years
Correct Answer: B
An increase of 2 in the average of 8 means the total rises by 16. The new person's age is 20 + 16 = 36.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 6 people is 30 years. Two people aged 24 and 36 are replaced by people aged 20 and 40. What is the new average age?
A. 30 years
B. 26 years
C. 33 years
D. 36 years
Correct Answer: A
The leaving ages total 60 and the joining ages also total 60. Therefore the total age and average remain unchanged at 30.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A family of four has an average age of 25 years. Five years later, a baby is born. What is the family's average age immediately after the birth?
A. 21 years
B. 26 years
C. 29 years
D. 24 years
Correct Answer: D
The current total is 4 × 25 = 100. Five years later the four members total 100 + 20 = 120. Including the newborn, the average is 120/5 = 24.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 12 employees is 29 years. When one employee leaves, the average of the remaining 11 becomes 28 years. What was the age of the employee who left?
A. 36 years
B. 43 years
C. 40 years
D. 46 years
Correct Answer: C
Original total = 12 × 29 = 348. Remaining total = 11 × 28 = 308. The employee's age was 348 - 308 = 40.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of 10 players is 24 years. When the captain joins, the average becomes 25 years. What is the captain's age?
A. 31 years
B. 35 years
C. 38 years
D. 41 years
Correct Answer: B
The players' total age is 10 × 24 = 240. With the captain, the total is 11 × 25 = 275. The captain's age is 275 - 240 = 35.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Five years ago, a father's age equaled the combined ages of his three children. The children's present ages are 12, 16 and 19 years. What is the father's present age?
A. 37 years
B. 33 years
C. 40 years
D. 43 years
Correct Answer: A
Five years ago, the children were 7, 11 and 14, totaling 32. The father was therefore 32 then, so his present age is 37.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father is 3 years older than the mother, and their son's age is one-third of the mother's age. Their total age is 94 years. What is the father's age?
A. 38 years
B. 45 years
C. 48 years
D. 42 years
Correct Answer: D
Let the mother's age be x. Then father = x + 3 and son = x/3. So x + x + 3 + x/3 = 94. This gives 7x/3 = 91, so x = 39 and father = 42.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother and two siblings have a total age of 96 years. The mother's age equals the combined ages of the siblings, who differ by 6 years. What is the elder sibling's age?
A. 24 years
B. 29 years
C. 27 years
D. 32 years
Correct Answer: C
The mother and children each account for half the total, so the siblings total 48. Two ages totaling 48 and differing by 6 are 21 and 27.