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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

10. At present, the ratio between the ages of Akbar and Denial is 4:3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present?
 
  • A. 5
  • B. 10
  • C. 15
  • D. 20
Ans: C.
Sol.
Let the present ages of Akbar and Danial be 4x years and 3x years respectively. Then,
4x + 6 =26 ⇔ 4x = 20 ⇔ x = 5.
∴ Deepak’s age = 3x =15 years.
 
11. The difference between the ages of two persons is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is
 
  • A. 25 years
  • B. 30 years
  • C. 35 years
  • D. 40 years
Ans: C.
Sol.
Let their ages of x years and (x + 10) years respectively.
Then, (x + 10) - 15 = 2(x - 15)
⇔ x - 5 = 2x - 30
⇔ x = 25.
∴ Present age of the elder person = (x + 10)
= 35 years.
 
 
12. Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
 
  • A. 2 years
  • B. 4 years
  • C. 6 years
  • D. 8 years
Ans: C.
Sol.
Mother's age when Ayesha's brother was born = 36 years.
Father's age when Ayesha's brother was born = (38 + 4) years
= 42 years.
∴ Required difference = (42 - 36) years = 6 years.