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PROBLEMS ON AGES

Aptitude

PROBLEMS ON AGES -> SOLVED EXAMPLES

1. Rabert’s age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev?
  Sol. Let Rabert’s present age be x years. Then,
Rabert’s age after 15 years = (x + 15) years.
Rabert’s age 5 years back = (x - 5) years.
∴ x + 15 = 5 (x - 5) ⇔ x + 15 = 5x - 25
⇔ 4x = 40 ⇔ x = 10.
Hence, Rabert’ present age = 10 years.
2. The present age of a father is 3 years more than three times the age of his son. Three years hence, father’s age will be 10 years more than twice the age of the son. Find the present age of the father.
  Sol. Let the son’s present age be x years. Then father’s present age = (3x + 3) years.
∴ (3x + 3 + 3) = 2 (x + 3) + 10 ⇔ 3x + 6 = 2x + 16 ⇔ x = 10.
Hence, father’s present age = (3x + 3) = (3x + 3) = (3 * 10 + 3) years = 33 years.
3. The ages of two persons differ by 16 years. If 6 years agao, the elder one be 3 times as old as the younger one, find their present ages.
  Sol.
Let the age of the younger person be x years.
Then, age of the elder perosn = (x + 16) years.
∴ 3(x - 6) = (x + 16 - 6) ⇔ 3x - 18 = x + 10
⇔ 2x = 28 ⇔ x = 14
Hence, their present ages are 14 years and 30 years.

PROBLEMS ON AGES -> Exercise

4. Four years ago, the father’s age was three times the age of his son. The total of the ages of the father and the son after four years, will be 64 years. What is the father’s age at present?
 
  • A. 32
  • B. 33
  • C. 36
  • D. 38
Ans: C.
Sol.
Let the ages of father and son 4 years ago be 3x and x years respectively.
Then, [(3x + 4) + 4] + [(x + 4) + 4] = 64 ⇔ 4x = 48 ⇔ x =12.
∴ Father’s present age = 3x = 36 years.
 
5. Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
 
  • A. 68
  • B. 108
  • C. 110
  • D. 126
Ans: B.
Sol.
Let the present ages of the father and son be 2x and x years respectively
Then, (2x - 18) = 3 (x - 18) ⇔ x = 36.
∴ Required sum = (2x + x) = 3x = 108 years.
 
 
6. A man is 24 years older than his son. In tow years, his age will be twice the age of his son. The present age of the son is:
 
  • A. 22
  • B. 24
  • C. 26
  • D. 42
Ans: A.
Sol.
Let the son’s present age be x years. Then, man’s present age = (x + 24) years.
∴ (x + 24) + 2 = 2(x + 2) ⇔ x + 26 = 2x + 4 ⇔ x = 22.