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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

22. A father is said to his son, “ I was as old as you, are at present at the time of your birth.” If the father's age is 38 years now, the son's age five years back was
 
  • A. 14 years
  • B. 19 years
  • C. 33 years
  • D. 38 years
Ans: A.
Sol.
Let the son's present age be x years.
Then, (38 - x) = x ⇔ 2x = 38
⇔ x = 19.
∴ Son's age 5 years back = (19 - 5) = 14 years.
 
23. Rajesh is 40 years old and Rohan is 60 years old. How many years ago was the ratio of their ages 3 : 5?
 
  • A. 5 years
  • B. 10 years
  • C. 20 years
  • D. 25 years
Ans: B.
Sol.
Suppose, the ratio was 3 : 5, x years ago.
Then, 40-x/60-x = 3/5
⇔ 5(40 - x)= 3(60 - x)
⇔ 2x = 20
⇔ x = 10.
 
 
24. The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is
 
  • A. 5 : 2
  • B. 7 : 3
  • C. 9 : 2
  • D. 13 : 4
Ans: B.
Sol.
Let the ages of father and son 10 years ago was 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x+10) + 10]
⇔ 3x + 20 = 2x + 40
⇔ x = 20.
∴ Required ratio = (3x + 10) : (x + 10)
= 70 : 30 ⇔ 7 : 3.