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.
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.