Age Problems Competitive Exams
50 questions · Mathematics
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Question 1 of 50
Ali is 7 years younger than Sara. The sum of their ages is 43 years. Sara's age is:
ExplanationLet Sara = x. Then x + (x − 7) = 43, so 2x = 50 and x = 25.
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Question 2 of 50
The ages of two friends are in the ratio 2 : 3 and their sum is 45 years. The age of the younger is:
ExplanationTotal parts = 5, so one part = 9. Younger = 2 × 9 = 18.
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Question 3 of 50
A is 4 years older than B and B is 4 years older than C. The sum of their ages is 54 years. A's age is:
ExplanationLet C = x, B = x + 4, A = x + 8. 3x + 12 = 54, so x = 14 and A = 22.
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Question 4 of 50
A man is 4 times as old as his son. After 16 years he will be twice as old as his son. The man's present age is:
ExplanationLet son = x. 4x + 16 = 2(x + 16), so 2x = 16, x = 8 and the man is 32.
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Question 5 of 50
Three siblings have ages in the ratio 2 : 3 : 5 and the sum of their ages is 50 years. The age of the middle sibling is:
ExplanationTotal parts = 10, so one part = 5. Middle = 3 × 5 = 15.
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Question 6 of 50
The ratio of the ages of A and B is 4 : 5 and the sum of their ages is 63 years. B's age is:
ExplanationTotal parts = 9, so one part = 7. B = 5 × 7 = 35.
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Question 7 of 50
The ratio of ages of A and B is 3 : 4 and of B and C is 2 : 3. The sum of their ages is 65 years. C's age is:
ExplanationB : C = 2 : 3 = 4 : 6, so A : B : C = 3 : 4 : 6. Total parts = 13, one part = 5. C = 6 × 5 = 30.
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Question 8 of 50
The sum of the present ages of three persons is 120 years. Ten years ago their ages were in the ratio 1 : 2 : 3. The present age of the eldest is:
ExplanationTen years ago the sum was 120 − 30 = 90, so one part = 15 and the ages were 15, 30, 45. Now they are 25, 40, 55.
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Question 9 of 50
A is 5 years older than B and the sum of their ages is 35 years. B's age is:
ExplanationLet B = x. Then x + (x + 5) = 35, so 2x = 30 and x = 15.
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Question 10 of 50
The ratio of the ages of Ali and Sara is 5 : 7. If Sara is 28 years old, Ali's age is:
ExplanationOne part = 28 ÷ 7 = 4. Ali = 5 × 4 = 20.
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Question 11 of 50
The sum of the ages of five children born at intervals of 3 years each is 50 years. The age of the eldest is:
ExplanationLet youngest = x. 5x + (3 + 6 + 9 + 12) = 50, so 5x = 20 and x = 4. Eldest = 4 + 12 = 16.
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Question 12 of 50
Reena is 5 years older than Seema. Seema is half the age of Teena. If Teena is 24 years old, Reena's age is:
ExplanationSeema = 24 ÷ 2 = 12. Reena = 12 + 5 = 17.
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Question 13 of 50
The ratio of ages of a mother and her daughter is 5 : 2. The mother is 27 years older. The daughter's age is:
ExplanationDifference = 3 parts = 27, so one part = 9. Daughter = 2 × 9 = 18.
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Question 14 of 50
The product of the ages of two sisters is 143 and the difference is 2 years. The sum of their ages is:
Explanation143 = 11 × 13 and 13 − 11 = 2, so the ages are 11 and 13. Sum = 24.
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Question 15 of 50
Five years ago a man was 7 times as old as his son. After five years he will be 3 times as old as his son. The man's present age is:
ExplanationLet son = x and man = m. m − 5 = 7(x − 5) and m + 5 = 3(x + 5). Solving: x = 10 and m = 40.
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Question 16 of 50
A is 6 years older than B. Four years ago A's age was twice B's age. A's present age is:
ExplanationLet B = x, A = x + 6. x + 2 = 2(x − 4), so x = 10. A = 16.
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Question 17 of 50
The average of the ages of three persons is 25 years. Two of them are 20 and 24 years old. The age of the third is:
ExplanationTotal = 75. Third = 75 − 20 − 24 = 31.
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Question 18 of 50
Twice a person's age plus 6 years is 50 years. The person's age is:
Explanation2x + 6 = 50 gives 2x = 44 and x = 22.
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Question 19 of 50
A man's age is 125% of his wife's age. If the wife is 40 years old, the man's age is:
Explanation125% of 40 = 1.25 × 40 = 50.
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Question 20 of 50
A man is 24 years older than his son. In two years his age will be twice his son's age. The son's present age is:
ExplanationLet son = x. x + 26 = 2(x + 2), so x = 22. The man is 46.
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Question 21 of 50
The average age of a family of 5 is 28 years. If the youngest member is 8 years old, the average age of the other four is:
ExplanationTotal = 140. Without the youngest, total = 132, so average = 132 ÷ 4 = 33.
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Question 22 of 50
The average age of 30 students is 15 years. When the teacher's age is included, the average becomes 16 years. The teacher's age is:
ExplanationTotal with teacher = 31 × 16 = 496. Students' total = 30 × 15 = 450. Teacher = 496 − 450 = 46.
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Question 23 of 50
The ratio of ages of two persons is 4 : 3 and the difference is 8 years. The sum of their ages is:
ExplanationDifference = 1 part = 8. Ages are 32 and 24, so the sum = 56.
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Question 24 of 50
Three sisters are each 4 years younger than the next older one. The sum of their ages is 60 years. The eldest sister's age is:
ExplanationLet youngest = x. Then x + (x + 4) + (x + 8) = 60, so 3x = 48 and x = 16. The eldest is 16 + 8 = 24.
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Question 25 of 50
The average age of 4 friends is 20 years. A 25-year-old joins them. The new average age is:
ExplanationOriginal total = 4 × 20 = 80. New total = 105 for 5 people, so the average = 21.
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Question 26 of 50
The ratio of ages of a father and his son is 7 : 2 and the difference is 30 years. The father's age is:
ExplanationDifference = 5 parts = 30, so one part = 6. Father = 7 × 6 = 42.
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Question 27 of 50
The sum of the ages of two brothers is 28 years and one is 6 years older than the other. The older brother's age is:
ExplanationLet younger = x. Then x + (x + 6) = 28, so x = 11 and the older is 17.
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Question 28 of 50
A grandfather is 66 years old, his son is 38 and his grandson is 10. After how many years will the sum of the ages of the son and grandson equal the grandfather's age?
Explanation38 + 10 + 2x = 66 + x, so x = 18. Check: 56 + 28 = 84 = 66 + 18.
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Question 29 of 50
A father is 3 times as old as his son. The sum of their ages is 48 years. The son's age is:
ExplanationLet son = x. Then x + 3x = 48, so 4x = 48 and x = 12.
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Question 30 of 50
The average age of 8 men increases by 2 years when one man aged 20 is replaced by a new man. The age of the new man is:
ExplanationTotal age increases by 8 × 2 = 16. New man = 20 + 16 = 36.
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Question 31 of 50
A mother is 4 times as old as her daughter. Four years ago she was 7 times as old. The mother's present age is:
ExplanationLet daughter = x. 4x − 4 = 7(x − 4), so 3x = 24, x = 8 and the mother is 32.
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Question 32 of 50
A father is 3 times as old as his son. After 10 years he will be twice as old as his son. The son's present age is:
ExplanationLet son = x. Then 3x + 10 = 2(x + 10), so x = 10. Check: father 30 and son 10 now; in 10 years 40 and 20.
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Question 33 of 50
Sara is 14 years old. Her age after 9 years equals her mother's age 11 years ago. The mother's present age is:
ExplanationSara after 9 years = 23. Mother's age 11 years ago = 23, so her present age = 23 + 11 = 34.
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Question 34 of 50
A mother is 24 years older than her daughter. The sum of their ages is 50 years. The daughter's age is:
ExplanationLet daughter = x. Then x + (x + 24) = 50, so 2x = 26 and x = 13.
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Question 35 of 50
The present ages of A and B are in the ratio 5 : 3. After 6 years the ratio will be 7 : 5. A's present age is:
Explanation(5x + 6)/(3x + 6) = 7/5 gives 25x + 30 = 21x + 42, so x = 3. A = 5 × 3 = 15.
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Question 36 of 50
The sum of the present ages of a father and his son is 45 years. The sum of their ages after 5 years will be:
ExplanationEach person grows 5 years older, so the sum rises by 2 × 5 = 10. New sum = 55.
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Question 37 of 50
Ayesha's age is 60% of her mother's age. If her mother is 50 years old, Ayesha's age after 10 years will be:
Explanation60% of 50 = 30. After 10 years she will be 30 + 10 = 40.
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Question 38 of 50
After 12 years A will be twice as old as he was 3 years ago. A's present age is:
Explanationx + 12 = 2(x − 3) gives x + 12 = 2x − 6, so x = 18.
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Question 39 of 50
The average age of a father, mother and son is 30 years. The average age of the father and mother is 40 years. The son's age is:
ExplanationTotal of three = 90. Parents' total = 80. Son = 90 − 80 = 10.
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Question 40 of 50
The ages of two persons are in the ratio 3 : 5 and their sum is 40 years. The age of the elder is:
ExplanationTotal parts = 8, so one part = 5. Elder = 5 × 5 = 25.
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Question 41 of 50
Ahmed is twice as old as Bilal and the difference of their ages is 14 years. Ahmed's age is:
ExplanationLet Bilal = x. Then 2x − x = 14, so x = 14 and Ahmed = 28.
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Question 42 of 50
The average age of 6 friends is 22 years. When one friend leaves, the average becomes 21 years. The age of the friend who left is:
ExplanationTotal of 6 = 132. Total of 5 = 105. Age of the friend = 132 − 105 = 27.
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Question 43 of 50
Three times Rina's age minus 5 years equals 22 years. Rina's age is:
Explanation3x − 5 = 22 gives 3x = 27 and x = 9.
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Question 44 of 50
A father is 40 years old and his son is 10. After how many years will the father be exactly twice as old as the son?
Explanation40 + x = 2(10 + x) gives 40 + x = 20 + 2x, so x = 20.
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Question 45 of 50
B is 9 years older than A. Ten years ago A's age was half of B's age. B's present age is:
ExplanationLet A = x, B = x + 9. x − 10 = (x − 1)/2, so 2x − 20 = x − 1 and x = 19. B = 28.
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Question 46 of 50
A is twice as old as B and B is 3 times as old as C. The sum of their ages is 90 years. A's age is:
ExplanationLet C = x, B = 3x, A = 6x. 10x = 90, so x = 9 and A = 54.
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Question 47 of 50
Ali is 4 years younger than Sara and Sara's age is 5/4 of Ali's age. Sara's age is:
ExplanationLet Ali = x. x + 4 = 5x/4, so 4x + 16 = 5x and x = 16. Sara = 20.
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Question 48 of 50
The ratio of ages of a father and son is 6 : 1 and the sum of their ages is 70 years. The son's age is:
ExplanationTotal parts = 7, so one part = 10. Son = 10.
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Question 49 of 50
Karim is 12 years old and this is one-fourth of his father's age. After how many years will the father be 3 times as old as Karim?
ExplanationFather = 48. 48 + x = 3(12 + x), so 12 = 2x and x = 6.
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Question 50 of 50
A boy's age is one-third of his father's age. The father is 24 years older than the boy. The father's age is:
ExplanationLet boy = x, father = 3x. Then 3x − x = 24, so x = 12 and the father is 36.
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