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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. 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. 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

1. Peter got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Peter’s sister was 10 years younger to him at the time of his marriage. The age of Peer’s sister is:

• A. 32
• B. 36
• C. 38
• D. 39
 Ans: C. Sol. Let Peter’s present age be x years. Then, his age at the time of marriage = (x - 8) years. ∴ x = 6/5 (x - 8) ⇔ 5x = 6x - 48 ⇔ x = 48. Peter’s sister’s age at the time of his marriage = (x - 8) - 10 = (x - 18) = 30 years. ∴ Peter’s sister’s present age = (30 + 8) years = 38 years.

2. The age of a man is three times the sum of the ages of his two sons. Five years hence, his age will be double of the some of the ages of his sons. The father’s present age is :

• A. 29 years
• B. 36 years
• C. 42 years
• D. 45 years
 Ans: D. Sol. Let the sum of present ages of the two sons be x years. Then, faher’s present age = 3x years. ∴ (3x + 5) = 2 (x + 10) ⇔ 3x + 5 = 2x + 20 ⇔ x = 15. Hence, father’s present age = 45 years.

3. The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?

• A. C is younger than A
• B. 6
• C. 12
• D. 24
 Ans: C. Sol. (A + B) - (B + C) = 12 ⇔ A - C = 12.