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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

13. The ratio between the present ages of P and Q is 6 : 7. If Q is 4 years old than P, what will be the ratio of the ages of P and Q after 4 years?
 
  • A. 3 : 4
  • B. 3 : 5
  • C. 4 : 3
  • D. 7 : 8
Ans: D.
Sol.
Let P's age and Q's age be 6x years and 7x years respectively.
Then, 7x - 6x = 4 ⇔ x = 4.
∴ Required ratio = (6x + 4) : (7x + 4) = 28 : 32 = 7 : 8.
 
14. Q is much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?
 
  • A. 1 year
  • B. 2 year
  • C. 25 year
  • D. Data inadequate
Ans: D.
Sol.
R - Q = R - T ⇒ Q = T.
Also, R + T = 50 ⇒ R + Q = 50.
So, (R - Q) cannot be determined.
 
 
15. The total of the ages of Jai, Prajan and Sarath is 93 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Sarath?
 
  • A. 24 years
  • B. 32 years
  • C. 38 years
  • D. 42 years
Ans: C.
Sol.
Let the ages of Jai, Prajan and Sarath 10 years ago be 2x, 3x and 4x years respectively.
Then, (2x + 10) + (3x + 10) + (4x + 10) = 93
⇔ 9x = 63
⇔ x = 7.
∴ Sarath's present age = (4x +10) = 38 years.