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, 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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Q. E is 5 years older than F. If F is 15 years old, how old is E?

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

Solution

If F is 15 years old, then E is 15 + 5 = 20 years old.

Correct Answer: B — 20

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Q. Five years ago, E was three times as old as F. If F is currently 10 years old, how old is E now?

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

Solution

Five years ago, F was 5 years old. So, E was 3 * 5 = 15 years old then. Now, E is 15 + 5 = 20 years old.

Correct Answer: B — 20

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Q. G is 3 years older than H. If the sum of their ages is 45 years, how old is H?

A. 20
B. 21
C. 22
D. 23

Solution

Let H's age be x. Then G's age is x + 3. So, x + (x + 3) = 45. Solving gives x = 21.

Correct Answer: B — 21

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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

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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

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Q. If I is 10 years older than J and the sum of their ages is 70 years, how old is I?

A. 30
B. 35
C. 40
D. 45

Solution

Let J's age be x. Then I's age is x + 10. So, x + (x + 10) = 70. Solving gives x = 30, hence I = 40.

Correct Answer: C — 40

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Q. If I is 3 years older than J and the sum of their ages is 45 years, what is I's age?

A. 21
B. 22
C. 23
D. 24

Solution

Let J's age be x. Then I's age is x + 3. So, x + (x + 3) = 45. Solving gives x = 21, thus I = 24.

Correct Answer: C — 23

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Q. If I is 5 years older than J and the sum of their ages is 45, what is J's age?

A. 20
B. 22
C. 25
D. 23

Solution

Let J's age be x. Then I's age is x + 5. So, x + (x + 5) = 45. Solving gives x = 20.

Correct Answer: B — 22

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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

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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

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Problems on Ages

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