Problems on Ages: Mastering Competitive Exam Concepts

Problems on Ages

Q. Ten years ago, a woman was 3 times as old as her son. If the son is now 10 years old, how old is the woman now?

A. 30
B. 40
C. 50
D. 60

Solution

Ten years ago, the son was 0 years old. Therefore, the woman was 3 * 0 = 0 years old. Now, she is 10 + 10 = 20 years old.

Correct Answer: B — 40

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Q. Ten years ago, the age of a man was 3 times the age of his son. If the son is now 10 years old, how old is the man now?

A. 30
B. 40
C. 50
D. 60

Solution

Ten years ago, the son was 10 - 10 = 0 years old. The man was 3 * 0 = 0 years old then, so now he is 10 + 30 = 40 years old.

Correct Answer: B — 40

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Q. Ten years ago, the age of A was three times the age of B. If B is now 15 years old, how old is A now?

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

Solution

Ten years ago, B was 15 - 10 = 5 years old. A was 3 * 5 = 15 years old then, so A is now 15 + 10 = 25.

Correct Answer: B — 30

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Q. Ten years ago, the age of A was twice the age of B. If A is now 30 years old, how old is B now?

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

Solution

Ten years ago, A was 30 - 10 = 20 years old. Therefore, B was 20 / 2 = 10 years old then. Now, B is 10 + 10 = 20 years old.

Correct Answer: D — 25

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Q. Ten years ago, the age of G was half of H's age. If H is now 30 years old, how old is G now?

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

Solution

Ten years ago, H was 20 years old. Therefore, G was 10 years old. Now, G is 10 + 10 = 20 years old.

Correct Answer: C — 25

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Q. The age of a father is twice the age of his son. If the sum of their ages is 60 years, how old is the son?

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

Solution

Let the son's age be x. Then the father's age is 2x. The equation is x + 2x = 60, which simplifies to 3x = 60, so x = 20.

Correct Answer: B — 25

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Q. The age of a grandfather is 3 times the age of his grandson. If the grandfather is 60 years old, how old is the grandson?

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

Solution

If the grandfather is 60 years old, then the grandson is 60 / 3 = 20 years old.

Correct Answer: B — 20

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Q. The age of a grandfather is 3 times the age of his grandson. If the grandson is 15 years old, how old is the grandfather?

A. 30
B. 45
C. 60
D. 75

Solution

If the grandson is 15 years old, then the grandfather is 3 * 15 = 45 years old.

Correct Answer: C — 60

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Q. The age of a grandfather is 4 times the age of his grandson. If the grandson is 8 years old, what is the grandfather's age?

A. 24
B. 32
C. 36
D. 40

Solution

If the grandson is 8 years old, then the grandfather is 4 * 8 = 32 years old.

Correct Answer: B — 32

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Q. The age of a grandfather is 4 times the age of his grandson. If the grandson is 8 years old, how old is the grandfather?

A. 24
B. 32
C. 36
D. 40

Solution

If the grandson is 8 years old, then the grandfather is 4 * 8 = 32 years old.

Correct Answer: B — 32

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Q. The age of a grandfather is three times the age of his grandson. If the grandson is 12 years old, what is the grandfather's age?

A. 30
B. 36
C. 40
D. 42

Solution

If the grandson is 12, then the grandfather is 3 * 12 = 36 years old.

Correct Answer: B — 36

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Q. The age of a man is 5 years more than twice the age of his son. If the son is 10 years old, how old is the man?

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

Solution

If the son is 10 years old, then the man's age is 2 * 10 + 5 = 25 years.

Correct Answer: C — 30

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Q. The age of a mother is 4 times that of her daughter. If the daughter is 8 years old, what is the mother's age?

A. 24
B. 32
C. 36
D. 40

Solution

If the daughter is 8 years old, then the mother is 4 * 8 = 32 years old.

Correct Answer: A — 24

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Q. The age of a mother is 4 times the age of her daughter. If the daughter is 5 years old, how old is the mother?

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: B — 20

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Q. The age of a mother is 4 times the age of her daughter. If the daughter is 6 years old, how old is the mother?

A. 18
B. 20
C. 24
D. 30

Solution

If the daughter is 6 years old, then the mother is 4 * 6 = 24 years old.

Correct Answer: C — 24

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Q. The age of a mother is 5 times the age of her daughter. If the daughter is 6 years old, what is the mother's age?

A. 24
B. 30
C. 36
D. 40

Solution

If the daughter is 6 years old, then the mother is 5 * 6 = 30 years old.

Correct Answer: A — 24

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Q. The age of I is three times the age of J. If the difference in their ages is 24 years, how old is J?

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

Solution

Let J's age be x. Then I's age is 3x. The difference is 3x - x = 24, hence 2x = 24, x = 12. Therefore, J is 12 years old.

Correct Answer: C — 16

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Q. The ages of M and N are in the ratio 5:3. If the sum of their ages is 64 years, what is M's age?

A. 30
B. 32
C. 34
D. 36

Solution

Let M's age be 5x and N's age be 3x. Then 5x + 3x = 64. Solving gives x = 8, thus M = 40.

Correct Answer: B — 32

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Q. The ages of O and P are in the ratio 5:3. If the sum of their ages is 64, what is O's age?

A. 40
B. 32
C. 36
D. 28

Solution

Let O's age be 5x and P's age be 3x. Then, 5x + 3x = 64. Solving gives x = 8, O's age = 5 * 8 = 40.

Correct Answer: A — 40

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Q. The combined age of O and P is 80 years. If O is 10 years older than P, how old is O?

A. 35
B. 40
C. 45
D. 50

Solution

Let P's age be x. Then O's age is x + 10. So, x + (x + 10) = 80. Solving gives x = 35, hence O = 45.

Correct Answer: B — 40

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Q. The present age of a grandfather is 4 times that of his grandson. If the grandson is 5 years old, what is the grandfather's age?

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

Solution

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

Correct Answer: D — 30

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Q. The ratio of the ages of G and H is 3:2. If G is 30 years old, how old is H?

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

Solution

If G is 30 years old, then H's age is (2/3) * 30 = 20 years.

Correct Answer: A — 20

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Q. The ratio of the ages of G and H is 3:4. If H is 32 years old, how old is G?

A. 24
B. 30
C. 28
D. 20

Solution

If H is 32 years, then G's age = (3/4) * 32 = 24 years.

Correct Answer: A — 24

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Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, how old is A?

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

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20, hence A = 30.

Correct Answer: C — 30

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Q. The sum of the ages of A and B is 50 years. If A is 10 years older than B, what is B's age?

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

Solution

Let B's age be x. Then A's age is x + 10. So, x + (x + 10) = 50. Solving gives x = 20.

Correct Answer: B — 25

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Q. The sum of the ages of a father and his son is 50 years. If the father is 30 years older than the son, how old is the son?

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

Solution

Let the son's age be x. Then the father's age is x + 30. So, x + (x + 30) = 50. Solving gives x = 10.

Correct Answer: C — 20

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Q. The sum of the ages of a father and his son is 50 years. If the father is 40 years old, how old is the son?

A. 10
B. 15
C. 20
D. 30

Solution

If the father is 40 years old, then the son is 50 - 40 = 10 years old.

Correct Answer: C — 20

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Q. The sum of the ages of a mother and her daughter is 50 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 10
B. 8
C. 12
D. 6

Solution

Let the daughter's age be x. Then the mother's age is 4x. The equation is x + 4x = 50, which simplifies to 5x = 50, so x = 10.

Correct Answer: A — 10

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Q. The sum of the ages of a mother and her daughter is 60 years. If the mother is 4 times as old as her daughter, how old is the daughter?

A. 8
B. 10
C. 12
D. 15

Solution

Let the daughter's age be x. Then the mother's age is 4x. So, x + 4x = 60. Solving gives x = 12.

Correct Answer: B — 10

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Q. Three years ago, a man was 5 times as old as his son. If the man is currently 38 years old, how old is his son now?

A. 6
B. 7
C. 8
D. 9

Solution

Let the son's age be x. Three years ago, the man was 35 and the son was x - 3. So, 35 = 5(x - 3). Solving gives x = 8.

Correct Answer: C — 8

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Problems on Ages

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