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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

16. A person was asked to state his age in years. His reply was, “Take my age three years hence, multiply it by 3 and then subtract three times my age three years ago and you will you know how old I am.” What was the age of the person?
 
  • A. 18 years
  • B. 20 years
  • C. 24 years
  • D. 32 years
Ans: A.
Sol.
Let the present age of the persons be x years.
Then, 3(x +3) - 3(x - 3) = x
⇔ (3x + 9) - (3x -9) = x
⇔ x = 18.
 
17. The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
 
  • A. 4 years
  • B. 6 years
  • C. 8 years
  • D. 10 years
Ans: A.
Sol.
Let the ages of the children be x, (x+3), (x+6), (x+9) and (x+12) years.
Then, x + (x+3) +(x+6) + (x+9) + (x+12) = 50
⇔ 5x = 20
⇔ x = 4 years.
∴ Age of the youngest child = x = 4 years.
 
 
18. The ratio between the present ages of P and Q is 5 : 7 respectively. If the difference between Q's present age and P's age after 6 years is 2, what is the total of P's and Q's present age?
 
  • A. 24 years
  • B. 36 years
  • C. 48 years
  • D. 52 years
Ans: C.
Sol.
Let the present ages of P and Q be 5x years and 7x years respectively.
Then, 7x - (5x + 6) = 2
⇔ 2x = 8
⇔ x = 4.
∴ Required sum = 5x + 7x = 12x = 48 years.