# Problems on Ages

Q21. The ratio of the ages of Ajay and Binod is 3 : 4. After 5 years, the new ratio of their ages will be 4 : 5. What is the age of Ajay present ?

(a) 10 years

(b) 13 years

(c) 15 years

(d) 19 years

**Answer:** (c) 15 years

Let, the present ages of Ajay and Binod are 3x and 4x

A/Q | 3x + 5 | = | 4 |

4x + 5 | 5 |

⇒ 15x + 25 = 16x + 20

⇒ x = 5

∴ Present age of Ajay = 3 X 5 = 15 years

Q22. 15 years hence a man will be just 3 times as old as he was 15 years ago. His present age is

(a) 22 years

(b) 25 years

(c) 29 years

(d) 30 years

**Answer:** (d) 30 years

Let the present age of the man be x years

A/Q x + 15 = 3 (x - 15)

⇒ x + 15 = 3x - 45

⇒ 2x = 60

⇒ x = 30 years

Q23. The present age of rahim is four times the age of his son. Five years ago, the age of Rahim was ten times the age of his son at that time. How old is the son at present ?

(a) 7.5 years

(b) 8.5 years

(c) 9.5 years

(d) 10 years

**Answer:** (a) 7.5 years

Let the present age of son be x years

∴ the present age of Rahim be 4x years

A/Q (x - 5) 10 = 4x - 5

⇒ 10x - 50 = 4x - 5

⇒ 6x = 50 - 5 = 45

⇒ x = ^{45}/_{6} = 7.5 years

Q24. A man's age is now three times that of his son. In 10 years, it will be double that of his son. The present age of the son is

(a) 10 years

(b) 12 years

(c) 13 years

(d) 15 years

**Answer:** (a) 10 years

Let, the present age of the son be x years

∴ The present age of the man be 3x years

A/Q (x + 10)2 = (3x + 10)

⇒ 2x + 20 = 3x + 10

⇒ x = 10 years

Q25. The present age of A, B, C are in the ratio 5:6:7. Five years ago, the sum of their ages was 75. Their present ages are

(a) 15, 20, 25 years

(b) 20, 25, 30 years

(c) 25, 30, 35 years

(d) 30, 35, 40 years

**Answer:** (c) 25, 30, 35 years

Let the present ages of A, B and C are 5x, 6x, 7x respectively

A/Q 5x - 5 + 6x - 5 + 7x - 5 = 75

⇒ 18x - 15 = 75

⇒ 18x = 75 + 15 = 90

⇒ x = ^{90}/_{18} = 5

∴ Their present ages are 5 X 5, 6 X 5, 7 X 5

i.e 25, 30, 35 years

Q26. The ratio of a man's age to his son's age is 5 : 1. The product of their ages is 80. The ratio of their ages after 5 years will be

(a) 19:7

(b) 23:9

(c) 23:7

(d) 25:9

**Answer:** (d) 25:9

Let the ages of man and his son be 5x, x

A/Q 5x X x = 80

⇒ 5x^{2} = 80

⇒ x^{2} = 16

⇒ x = 4

Man's present age = 5 X 4 = 20 years

Son's present age = 4 years

After 5 years their ratio 20+5 : 4+5 = 25 :9

Q27. Ram is 40 years old and Rahim is 60 years old. How many years ago was the ratio of their ages 3:5 ?

(a) 8 years

(b) 9 years

(c) 10 years

(d) 12 years

**Answer:** (c) 10 years

Let the required ages be x

A/Q | 40 - x | = | 3 |

60 - x | 5 |

⇒ 5(40 - x) = 3(60 - x)

⇒ 200 - 5x = 180 - 3x

⇒ 2x = 20

⇒ x = 10 years

Q28. The ratio between the present ages of Gita and Seema is 2:3. If Seema was 5 years older to Geeta four years back, how old is Geeta now ?

(a) 10 years

(b) 11 years

(c) 12 years

(d) 13 years

**Answer:** (a) 10 years

Let, the present ages of Geeta and Seema be 2x, 3x

(2x - 4) + 5 = 3x - 4

⇒ 2x - 4 + 5 = 3x - 4

⇒ 2x + 1 = 3x - 4

⇒ x = 5

∴ Present age of Gita = 2 X 5 = 10 years

Q29. A man's present age is three-seventh of the age of his mother. After 6 years, he will be one-half of the age of his mother at that time. How old is the man at present ?

(a) 14 years

(b) 15 years

(c) 16 years

(d) 18 years

**Answer:** (d) 18 years

Let, the present age of mother be x years

∴ the present age of the man be ^{3}?_{7} x years

A/Q ½(x + 6) = | 3 | x + 6 |

7 |

⇒ ½(x + 6) = | 3x + 42 |

7 |

⇒ 7x + 42 = 6x + 84

⇒ x = 84 - 42 = 42

∴ Man's present age = ^{3}/_{7} X 42 years = 18 years

Q30. Bimal is as much younger to Rahul as he is older to Nayan. If the total ages of Rahul and Nayan is 42 years, how old is Bimal ?

(a) 15 years

(b) 17 years

(c) 19 years

(d) 21 years

**Answer:** (d) 21 years

Rahul - Bimal = Bimal - Nayan

⇒ R - B = B - N

⇒ 2B = R + N

⇒ 2B = 42

⇒ B = 21 years