## Math Topic - Ages

Published in: Mathematics
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Helpful Notes for students who are preparing for competitive exams.

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PBI PBI INSTITUTE 1. AGES Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand's present age in years ? A. 24 c. 40. Solution B. 27 D. cannot be determined Let the present ages of sameer and anand be 5x years and 4x years respectively. Then Anands's present age x=6. =24 years. 2. 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 ages ? A. 46 years C. 52 years Solution B. 48 years D. 56 years Let the present ages of P and Q be 5x years and 7x years respectively. Then Required sum = 5x+7x years. 3. Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is A. 54. c. 105 Solution Let the present ages of Father and Son be 2x years and x years respectively. Then Required sum B. 72 D. 108 2x-18=3x-54 = (2x+x) =3x =3x36 = 108 years. 4. 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 when my brother was born, then, what was the age of my father and mother respectively when my
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PBI brother was born ? A. 32 yrs, 23 yrs C. 35 yrs, 29 yrs Solution PBI INSTITUTE B. 32 yrs, 29 yrs D. 35 yrs, 33 yrs Clearly,my mother was born 3 years before I was born and 4 years after my sister was born. So, father's age when brother was born mother's age when brother was born = 32 years. = 23 years. 5. 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 know how old I am." What was the age of the person ? A. 14 years C. 20 years Solution Let the present ages of the person be x years. B. 18 years D. 32 years Then 6. A father said to his son, "1 was as old as you are at present at the time of your birth." the father's age is 38 years now, the son's age five years back was If A. 14 years. C. 33 years Solution Let the son's present age be x years. Then Therefore son's age 5 years back B. D. 19 years 38 years =(19-5) years = 14 years.
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PBI PBI INSTITUTE 7. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is A. 14 years C. 20 years Solution Let the son's present age be x years. = (x + 24)years Then, man's present age B. D. (x + 24) =22 years. 18 years 22 years x(X+2) 8. 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 ? 4 years 10 years B. D. 8 years 12 years C. Solution Let the ages of the children be x,(X+3),(X+6),(X+9) and (x+12) years. Then, Age of the youngest child -4 years. 9. 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 C. 6years Solution Mother's age when Ayesha's brother was born Father's age when Ayesha's brother was born D. 4 years 12 years = 36 years.
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PBI Required difference PBI INSTITUTE = (38+4) years. = 42 years. = (42-36) = 6 years. 10. Sneh's ago is 1/6 th of her father's age. Sneh's father's age will be twice of Vimal's age after 10 years. If Vimal's eighth birthday was celebrated two years before, then what is Sneh's present age ? A. C. Solution 10 years 35 years B. D. = (8+2+10)years = 20 years. = 40 years = 30 years = (1/6 x 30)years = 5 years. 25 years None of these Vimal's age after 10 years Sneh's father age after 10 years Sneh's father Present age Therefore Sneh's age 11. A person's present age is two-fifth of the age of his mother. After 8 years, he will be one- half of the age of his mother. How old is the mother at present ? A. 32 years B. 36 years C. 40 years D. 48 years Solution Let the mother's present age be x years. Then, the person's = (2/5 x) years. present age Therefore = 1/2(X+8) = 2(2X+40)
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PBI PBI INSTITUTE = 40 years. 12. 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. C. Solution 3 B. Let PIs age and Qs age be 6x years and 7x years respectively. Then, Required ratio : (7X+4) = 28 : 32 13. Rajeev's age after 15 years will be 5 times his age 5 years back. What is the present age of Rajeev ? A. C. Solution 5 years 20 years B. D. 10 years 25 years Let Rajeev's present age be x years. Then Rajeev's age 15 years Rajeev's age 5 years back Therefore = (x+15) years. = (x-5) years. 5
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PBI 14 years 20 years C. Solution Let the son's present age be x years . Then, man's present age Then B. D. = (x+24)years. 2(X+2) 15. x: 22. Hitesh is 40 years old and Ronnie is 60 years old. ages 3 : 5? A. C. Solution 5 years 20 years B. D. PBI INSTITUTE 18 years 22 years How many years ago was the ratio of their 10 years 37 years Suppose, the ratio was 3 : 5, x years ago. Then, 16. Solution 40 -x/ 60 -x = 3/5. 20 10. The ages of two persons differ by 16 years. If 6 years ago, the elder one be 3 times as old as the younger one, find their present ages. C. 14 years 24 years B. D. 17 years 29 years Let the age of the younger person be x years. Then, age of the elder person = (x + 16) years.
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PBI IN Therefore PBI INSTITUTE 3 (x -6) 16-6) = 28 x= 14 years. 17. Solution The present ages of three persons are in proportions 4 : 7 :9. Eight years ago, the sum of their ages was 56. Find their present ages (in years) A. c. 8, 20, 28 20, 35, 45 B. D. 16, 28, 36 None of these Let their present ages be 4x,7x and 9x years respectively. Then, = 56 = 80 Their present ages are 16,28,36 years .

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