Problems on Ages: Mastering Competitive Exam Concepts

Problems on Ages

Q. A and B are of different ages. If A is 5 years older than B and the sum of their ages is 45, how old is A?

A. 20
B. 22
C. 25
D. 27

Solution

Let B's age be x. Then A's age is x + 5. So, x + (x + 5) = 45. Solving gives A = 25.

Correct Answer: C — 25

Q. A and B are of different ages. If A is 5 years older than B and the sum of their ages is 45, what is A's age?

A. 20
B. 22
C. 25
D. 27

Solution

Let B's age be x. Then A's age is x + 5. So, x + (x + 5) = 45. Solving gives A = 25.

Correct Answer: C — 25

Q. A father is 4 times as old as his son. If the sum of their ages is 50 years, how old is the father?

A. 40
B. 30
C. 20
D. 10

Solution

Let the son's age be x. Then the father's age is 4x. So, x + 4x = 50. Solving gives the father is 40.

Correct Answer: A — 40

Q. A father is three times as old as his son. If the father is 36 years old, how old is the son?

A. 12
B. 10
C. 15
D. 9

Solution

If the father is 36 years old and he is three times as old as his son, then the son's age is 36 / 3 = 12.

Correct Answer: A — 12

Q. A grandfather is 4 times as old as his grandson. If the grandson is 5 years old, how old is the grandfather?

A. 20
B. 15
C. 25
D. 30

Solution

If the grandson is 5 years old, then the grandfather's age is 4 * 5 = 20.

Correct Answer: A — 20

Q. A is 3 times as old as B. If the sum of their ages is 48 years, how old is A?

A. 36
B. 24
C. 12
D. 18

Solution

Let B's age be x. Then A's age is 3x. So, x + 3x = 48, which gives 4x = 48, hence x = 12. Therefore, A is 3 * 12 = 36 years old.

Correct Answer: A — 36

Q. A is 3 years older than B. If the sum of their ages is 27, how old is A?

A. 12
B. 15
C. 18
D. 21

Solution

Let B's age be x. Then A's age is x + 3. So, x + (x + 3) = 27. Solving gives x = 12. Therefore, A is 15.

Correct Answer: B — 15

Q. A is 3 years older than B. If the sum of their ages is 27, how old is B?

A. 10
B. 12
C. 13
D. 15

Solution

Let B's age be x. Then A's age is x + 3. So, x + (x + 3) = 27. Solving gives x = 12.

Correct Answer: B — 12

Q. A is 4 years older than B. If the sum of their ages is 28 years, how old is A?

A. 12
B. 14
C. 16
D. 18

Solution

Let B's age be x. Then A's age is x + 4. So, x + (x + 4) = 28. Solving gives x = 12, so A = 16.

Correct Answer: C — 16

Q. A is 5 years older than B. If the sum of their ages is 45 years, how old is B?

A. 20
B. 22
C. 25
D. 30

Solution

Let B's age be x. Then A's age is x + 5. So, x + (x + 5) = 45, which gives 2x + 5 = 45, hence 2x = 40, x = 20. Therefore, B is 20 years old.

Correct Answer: B — 22

Q. A is twice as old as B. If B is 10 years old, how old is A?

A. 10
B. 15
C. 20
D. 25

Solution

If B is 10 years old, then A is 2 * 10 = 20 years old.

Correct Answer: C — 20

Q. A man is 10 years older than his wife. If the sum of their ages is 70 years, how old is the wife?

A. 30
B. 25
C. 35
D. 40

Solution

Let the wife's age be x. Then the man's age is x + 10. The equation is x + (x + 10) = 70, which simplifies to 2x + 10 = 70, so 2x = 60, and x = 30.

Correct Answer: B — 25

Q. A man is 3 times as old as his son. If the sum of their ages is 48 years, how old is the son?

A. 8
B. 12
C. 16
D. 20

Solution

Let the son's age be x. Then the man's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. A mother is 21 years older than her daughter. If the daughter is 9 years old now, how old will the mother be in 5 years?

A. 25
B. 30
C. 35
D. 40

Solution

The mother is currently 9 + 21 = 30 years old. In 5 years, she will be 30 + 5 = 35.

Correct Answer: C — 35

Q. A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. What is the present age of the daughter?

A. 4
B. 8
C. 12
D. 16

Solution

Let the daughter's age be x. Then the mother's age is 4x. In 8 years, 4x + 8 = 2(x + 8). Solving gives x = 8.

Correct Answer: B — 8

Q. A mother is 4 times as old as her daughter. After 8 years, the mother will be twice as old as her daughter. How old is the daughter now?

A. 4
B. 8
C. 12
D. 16

Solution

Let the daughter's age be x. Then the mother's age is 4x. In 8 years, 4x + 8 = 2(x + 8). Solving gives x = 8.

Correct Answer: B — 8

Q. A woman is 3 years older than her brother. If the sum of their ages is 27 years, how old is the brother?

A. 12
B. 10
C. 15
D. 9

Solution

Let the brother's age be x. Then the woman's age is x + 3. The equation is x + (x + 3) = 27, which simplifies to 2x + 3 = 27, so 2x = 24, and x = 12.

Correct Answer: B — 10

Q. A woman is 5 years older than her sister. If the sister is 15 years old, how old is the woman?

A. 20
B. 25
C. 30
D. 35

Solution

If the sister is 15, then the woman is 15 + 5 = 20 years old.

Correct Answer: A — 20

Q. A's age is 2 years more than B's age. If the sum of their ages is 34, what is A's age?

A. 16
B. 18
C. 20
D. 22

Solution

Let B's age be x. Then A's age is x + 2. So, x + (x + 2) = 34, which gives 2x + 2 = 34, hence 2x = 32, x = 16. Therefore, A's age is 16 + 2 = 18.

Correct Answer: D — 22

Q. A's age is twice that of B's age. If the difference between their ages is 10 years, what is A's age?

A. 20
B. 25
C. 30
D. 35

Solution

Let B's age be x. Then A's age is 2x. The difference is 2x - x = 10, hence x = 10. So, A's age is 2 * 10 = 20.

Correct Answer: C — 30

Q. If A is 3 years older than B and B is 2 years younger than C, how old is C if A is 25 years old?

A. 24
B. 26
C. 27
D. 28

Solution

If A is 25 years old, then B is 25 - 3 = 22 years old. Since B is 2 years younger than C, C is 22 + 2 = 24 years old.

Correct Answer: B — 26

Q. If a mother is 6 times as old as her daughter now, and in 6 years, she will be 4 times as old as her daughter, how old is the daughter now?

A. 6
B. 4
C. 5
D. 3

Solution

Let the daughter's age be x. Then the mother's age is 6x. In 6 years, the mother will be 6x + 6 and the daughter will be x + 6. The equation is 6x + 6 = 4(x + 6), which simplifies to 6x + 6 = 4x + 24, so 2x = 18, and x = 9.

Correct Answer: C — 5

Q. If the age of a woman is 3 times the age of her daughter and the sum of their ages is 48, how old is the daughter?

A. 8
B. 12
C. 16
D. 20

Solution

Let the daughter's age be x. Then the woman's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. If the age of a woman is 3 times the age of her daughter and the sum of their ages is 48, what is the age of the daughter?

A. 8
B. 12
C. 16
D. 20

Solution

Let the daughter's age be x. Then the woman's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. If the present age of a father is 45 years and his son is 15 years old, in how many years will the father be twice as old as his son?

A. 10
B. 15
C. 20
D. 5

Solution

Let the number of years be x. In x years, the father's age will be 45 + x and the son's age will be 15 + x. The equation is 45 + x = 2(15 + x), which simplifies to 45 + x = 30 + 2x, so x = 15.

Correct Answer: A — 10

Q. If the present age of a grandfather is 80 years and the age of his grandson is 20 years, how many years ago was the grandfather 3 times as old as the grandson?

A. 10
B. 20
C. 30
D. 40

Solution

Let x years ago, grandfather's age was 80 - x and grandson's age was 20 - x. We need 80 - x = 3(20 - x). Solving gives x = 10.

Correct Answer: B — 20

Q. If the present age of a man is 3 times that of his son and the sum of their ages is 48 years, what is the age of the son?

A. 8
B. 12
C. 16
D. 20

Solution

Let the son's age be x. Then the man's age is 3x. So, x + 3x = 48. Solving gives x = 12.

Correct Answer: C — 16

Q. If the present age of a man is 4 times that of his son, and after 5 years, the man will be 3 times as old as his son. What is the present age of the son?

A. 5
B. 10
C. 15
D. 20

Solution

Let the son's age be x. Then the man's age is 4x. In 5 years, 4x + 5 = 3(x + 5). Solving gives x = 10.

Correct Answer: B — 10

Q. If the present age of a mother is 4 times that of her daughter and the daughter is 5 years old, what is the mother's age?

A. 15
B. 20
C. 25
D. 30

Solution

If the daughter is 5 years old, then the mother is 4 * 5 = 20 years old.

Correct Answer: C — 25

Q. If the present age of a mother is 4 times that of her son, and the son is 5 years old, what will be the mother's age in 5 years?

A. 20
B. 25
C. 30
D. 35

Solution

The mother is currently 4 * 5 = 20 years old. In 5 years, she will be 20 + 5 = 25 years old.

Correct Answer: B — 25

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