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.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A is 6 years younger than B. Five years from now, the sum of their ages will be 50. What is A's present age?
A. 22
B. 18
C. 15
D. 17
Correct Answer: D
Present sum=50−10=40. Let A=x and B=x+6. Then 2x+6=40, so x=17.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A person's age after 15 years will be four times the age 15 years ago. What is the present age?
A. 30
B. 25
C. 35
D. 20
Correct Answer: B
Let present age=x. x+15=4(x−15). Therefore x+15=4x−60, 3x=75, x=25.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of A, B and C are in the ratio 4:5:6. If C is 14 years older than A, what is B's age?
A. 28
B. 32
C. 42
D. 35
Correct Answer: D
C−A=2 parts=14, so one part=7. B=5×7=35.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A father is 28 years older than his son. Four years ago, he was three times as old as his son. What is the son's present age?
A. 16
B. 20
C. 18
D. 14
Correct Answer: C
Let son's age=x; father=x+28. Four years ago: x+24=3(x−4). Thus x=18.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The sum of two present ages is 50 years. After 5 years, the older person will be twice the younger. What is the younger person's present age?
A. 25
B. 15
C. 10
D. 20
Correct Answer: B
Let younger=x and older=50−x. After 5 years: 55−x=2(x+5). Thus 45=3x and x=15.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Six years ago, the ages of A and B were in the ratio 1:2. Six years from now, they will be in the ratio 2:3. What is B's present age?
A. 24
B. 36
C. 28
D. 30
Correct Answer: D
Six years ago ages were x and 2x. Present ages are x+6 and 2x+6. After six more years, (x+12)/(2x+12)=2/3, giving x=12; B=30.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The present ages of A and B are in the ratio 3:2. After 10 years, their ages will be in the ratio 4:3. What is A's present age?
A. 20
B. 24
C. 36
D. 30
Correct Answer: D
Let ages be 3x and 2x. (3x+10)/(2x+10)=4/3. Thus 9x+30=8x+40, x=10 and A=30.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
In 8 years, a person's age will be 1.5 times the present age. What is the present age?
A. 16
B. 12
C. 18
D. 24
Correct Answer: A
Let present age=x. x+8=1.5x, so 0.5x=8 and x=16.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
The ages of two people are in the ratio 5:3 and differ by 14 years. What is the older person's age?
A. 35
B. 42
C. 28
D. 30
Correct Answer: A
Difference of ratio parts=2. One part=14/2=7. Older age=5×7=35.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
Twelve years ago, a father was five times as old as his son. Presently, he is three times as old. What is the son's present age?
A. 18
B. 24
C. 30
D. 20
Correct Answer: B
Let son's age=x and father=3x. Twelve years ago: 3x−12=5(x−12). Solving gives x=24.
CSS - PMS - CCE - PCS - Mathematics
Age Problems
A person's age after 10 years will be twice the present age. What is the present age?
A. 5
B. 10
C. 20
D. 15
Correct Answer: B
Let present age be x. x+10=2x, so x=10 years.