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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

19. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

• A. 7
• B. 8
• C. 9
• D. 10
 Ans: D. Sol. Let C's age be x years. Then B's age = 2x years. A's age = (2x + 2) years. ∴ (2x +2) + 2x + x = 27 ∴ 5x = 25 ∴ x = 5. Hence, B's age = 2x = 10 years.

20. My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age of when my brother was born, then, what was the age of my father and mother respectively when my brother was born?

• A. 32 yrs, 23 yrs
• B. 32 yrs, 29 yrs
• C. 35 yrs, 29 yrs
• D. 35 yrs, 33 yrs
 Ans: A. Sol. Clearly, my brother was born 3 years before I was born and 4 years after my sister was born. So, father's age when brother was born = (28 + 4) = 32 years. mother's age when was born = (26 - 3) years = 23 years.

21. The ratio of the father's age to his son's age is 7 : 3. The product of their ages is 756. The ratio of their ages after 6 years will be

• A. 2 : 1
• B. 5 : 2
• C. 11 : 7
• D. 13 : 9
 Ans: A. Sol. Let the present ages of the father and son be 7x amd 3x years respectively. Then, 7x × 3x = 756 ⇔ 21x2 = 756 ⇔ x2 = 36 ⇔x = 6. ∴ Required ratio = (7x + 6) : (3x + 6) = 48 : 24 = 2 : 1.