CSS - PMS - CCE - PCS - Mathematics
Algebra
Solve: 3x + 5 = 20.
A. 3
B. 10
C. 5
D. 7
Correct Answer: C
3x=15, so x=5.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A woman is six times as old as a child. After 12 years, she will be three times as old. What is the woman's present age?
A. 42
B. 48
C. 54
D. 36
Correct Answer: B
Let child's age=x and woman's age=6x. After 12 years: 6x+12=3(x+12). Thus 3x=24, x=8 and woman=48.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Three years ago, the ages of A and B were in the ratio 4:3. Nine years from now, they will be in the ratio 7:6. What is A's present age?
A. 16
B. 21
C. 18
D. 19
Correct Answer: D
Three years ago ages were 4x and 3x. Nine years from now they are 4x+12 and 3x+12. Their ratio 7:6 gives x=4, so A=19.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of eight students is 15 years. When their teacher is included, the average becomes 18 years. What is the teacher's age?
A. 40
B. 36
C. 42
D. 45
Correct Answer: C
Students' total=8×15=120. New total=9×18=162. Teacher's age=42.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father and his two sons have a total age of 90 years. The father is twice the combined age of the sons, whose ages are in the ratio 2:3. What is the elder son's age?
A. 18
B. 20
C. 12
D. 15
Correct Answer: A
Let sons' total=S and father=2S. Then 3S=90, S=30. Sons are 2:3, so elder=3/5×30=18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Ten years from now, a person will be twice as old as five years ago. What is the present age?
A. 15
B. 25
C. 20
D. 30
Correct Answer: C
Let present age=x. x+10=2(x−5). Thus x+10=2x−10 and x=20.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 3:5. After 9 years, the ratio will be 2:3. What is B's present age?
A. 36
B. 40
C. 50
D. 45
Correct Answer: D
Let ages be 3x and 5x. (3x+9)/(5x+9)=2/3. Hence 9x+27=10x+18, x=9 and B=45.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A mother is 30 years older than her daughter. After 5 years, the mother will be 2.5 times as old. What is the daughter's present age?
A. 12
B. 15
C. 10
D. 20
Correct Answer: B
Let daughter=x; mother=x+30. After 5 years: x+35=2.5(x+5). Solving gives x=15.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A is twice as old as B. Eight years ago, A was three times as old as B. What is A's present age?
A. 32
B. 24
C. 36
D. 28
Correct Answer: A
Let B=x and A=2x. Eight years ago: 2x−8=3(x−8). Therefore x=16 and A=32.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of a husband and wife is 35 years. When their child is included, the average becomes 24 years. What is the child's age?
A. 1
B. 2
C. 4
D. 6
Correct Answer: B
Husband and wife total=70. Family total=3×24=72. Child's age=2 years.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of three siblings are in the ratio 3:4:5 and total 60 years. What will be their average age after 6 years?
A. 24
B. 28
C. 26
D. 20
Correct Answer: C
Present average=60/3=20. After 6 years, each age increases by 6, so average=26.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 6:5. Ten years ago, they were in the ratio 4:3. What is A's present age?
A. 24
B. 36
C. 25
D. 30
Correct Answer: D
Let ages be 6x and 5x. (6x−10)/(5x−10)=4/3. Thus 18x−30=20x−40, x=5 and A=30.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of A's and B's ages is 52 years. Four years from now, A will be 1.5 times as old as B. What is A's present age?
A. 32
B. 30
C. 28
D. 36
Correct Answer: A
Let B=x and A=52−x. Then 56−x=1.5(x+4). Solving gives x=20, so A=32.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father is four times as old as his daughter. Five years ago, he was seven times as old. What is the father's present age?
A. 35
B. 40
C. 45
D. 42
Correct Answer: B
Let daughter's age=x and father=4x. Five years ago: 4x−5=7(x−5). Thus 30=3x, x=10 and father=40.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Seven years from now, a person's age will be three times the age seven years ago. What is the present age?
A. 12
B. 21
C. 10
D. 14
Correct Answer: D
Let present age=x. x+7=3(x−7). So x+7=3x−21, 2x=28 and x=14.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 5:7. Four years ago, their ages totaled 40 years. What is B's present age?
A. 20
B. 28
C. 24
D. 32
Correct Answer: B
Present total=40+8=48. Ratio total=12 parts, one part=4. B=7×4=28.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The average age of four friends is 18 years. A fifth friend aged 28 joins them. What is the new average?
A. 22
B. 21
C. 19
D. 20
Correct Answer: D
Original total=4×18=72. New total=100. New average=100/5=20.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Three ages are in arithmetic progression and their sum is 72 years. What is the middle age?
A. 22
B. 26
C. 24
D. 18
Correct Answer: C
For three terms in arithmetic progression, the middle term equals their average. 72/3=24.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A grandfather is twice as old as the father, and the father is three times as old as the son. Their total age is 120 years. What is the father's age?
A. 36
B. 40
C. 48
D. 30
Correct Answer: A
Let son's age=x, father=3x, grandfather=6x. Total=10x=120, x=12, so father=36.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of two brothers are in the ratio 2:3. Eight years ago, their ages were in the ratio 1:2. What is the elder brother's present age?
A. 28
B. 24
C. 20
D. 16
Correct Answer: B
Let present ages be 2x and 3x. (2x−8)/(3x−8)=1/2. Hence 4x−16=3x−8, x=8 and elder=24.