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PROBLEMS ON AGES

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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

7. The sum of the present ages of a father and his son is 60 years. Six year ago, father’s age was five times the age fo the son. After 6 years, son’s age will be
 
  • A. 10
  • B. 15
  • C. 20
  • D. 30
Ans: C.
Sol.
Let the present age of son and father be x and (60 - x) years respectively.
Then, (60 - x) - 6 = 5 (x - 6) ⇔ 6x = 84 ⇔ x = 14.
∴ Son’s age after 6 years = (x + 6) = 20 years.
 
8. One year age, Promila was four times as old as her daughter Jenilia. Six years hence, Promila♥s age will exceed her daughter’s age by 9 years. The ratio of the present ages of Promila and her daughter is :
 
  • A. 13:4
  • B. 14:5
  • C. 15:5
  • D. 16:5
Ans: A.
Sol.
Let the ages of Promila and Jenilia 1 year ago be 4x and x years respectively.
Then, [(4x + 1) + 6] - [(x + 1) + 6] = 9 ⇔ 3x = 9 ⇔ x = 3.
∴ Required ratio = (4x + 1) : (x + 1) = 13:4.
 
 
9. The present ages of three persons are in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages (in years)
 
  • A. 12, 14, 18
  • B. 14, 20, 36
  • C. 16, 12, 14
  • D. 16, 28, 36
Ans: D.
Sol.
Let thier present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56 ⇔ 20x = 80 ⇔ x = 4.
∴ Their present ages are 16 years, 28 years and 36 years respectively.