# Problems on Ages

Q11. The ratio of Sampriti's age to the age of her mother is 4 : 13. The difference between their ages of 27 years. The ratio of the ages after 2 years will be

(a) 4 : 5

(b) 6 : 7

(c) 11 : 27

(d) 14 : 41

**Answer:** (d) 14 : 41

Let the ages of Sampriti and her mother be 4x and 13x years

A/Q 13x - 4x = 27

⇒ 9x = 27

⇒ x = 3

Ratio after 2 years = | 4x + 2 | = | 4 X 3 + 2 | = 14/41 = 14 : 41 |

13x + 2 | 13 X 3 + 2 |

Q12. The age of a man 10 years ago was thrice the age of his son. Ten years hence, the man's age will be twice that of his son. The ratio of their present ages is

(a) 7 : 3

(b) 9 : 5

(c) 11 : 7

(d) 13 : 9

**Answer:** (a) 7 : 3

Let the present age of the son be x years

Man's age 10 years ago = 3 (x - 10) = 3x - 30

Man's present age = (3x - 30 + 10) = 3x - 20

Man's age 10 years hence = 3x - 20 + 10 = 3x - 10

Son's age 10 years ago = x + 10

∴ 3x - 10 = 2(x + 10)

⇒ 3x - 2x = 20 + 10

⇒ x = 30

∴ Men's present age = 3 X 30 - 20 = 70 years

Son's present age = 30 years

∴ Ratio = 70 : 30 = 7 : 3

Q13. X is 26 years old and Y is 6 years. In how many years will X be twice as old as Y ?

(a) 10

(b) 11

(c) 14

(d) 15

**Answer:** (c) 14

Let the required age be x years

Now, 26 + x = 2 (6 + x)

⇒ 26 + x = 12 + 2x

⇒ x = 26 - 12 = 14

Q14. The sum of the ages of five chilndren born at the intervals of 2 years each is 50 years. What is the age of the youngest child ?

(a) 4

(b) 6

(c) 7

(d) 9

**Answer:** (b) 6

Let teh age of the youngest child be x years

Now x + (x+2) + (x+4) + (x+6) + (x+8) = 50

⇒ 5x + 20 = 50

⇒ x = 6

Q15. A is 2 years older than B who is twice as old as C. If the total of the ages of A, B, C be 52 years, then how old B is

(a) 14 years

(b) 17 years

(c) 20 years

(d) 23 years

**Answer:** (c) 20 years

Let the age of C be x years

∴ the age of B be 2x years

the age of A be 2x + 2

A/Q x + 2x + 2x + 2 = 52

⇒ 5x = 52 - 2

⇒ x = 10

B's age is 2 X 10 = 20 years

Q16. The difference between the present ages of Anil and Sunil is 5 years. The ratio between their ages after 6 yeyars will be 3 : 4. What can be the present age of Sunil ?

(a) 14 years

(b) 16 years

(c) 18 years

(d) 20 years

**Answer:** (a) 14 years

Let the age of Anil be x years

∴ the age of Sunil be x+5 years

A/Q | x + 6 | = | 3 |

x + 5 + 6 | 4 |

⇒ | x + 6 | = | 3 |

x + 11 | 4 |

⇒ 4x + 24 = 3x + 33

⇒ x = 9

∴ Present age of Sunil = 9 + 5 = 14 years

Q17. The product of Hari's age 5 years ago with his age 7 years later is 45. Hari's present age is

(a) 6 years

(b) 7 years

(c) 8 years

(d) 9 years

**Answer:** (c) 8 years

Let the Hari's present age be x years

A/Q (x - 5)(x + 7) = 45

⇒ x^{2} + 2x - 35 = 45

⇒ x^{2} + 2x - 80 = 0

⇒ x^{2} + 10x - 8x - 80 = 0

⇒ x(x + 10) - 8(x + 10) = 0

⇒ (x + 10) (x - 8) = 0

∴ x = 8 years

Q18. The ages of two persons are in the ratio of 5 : 7. 16 years ago, their ages were in the ratio of 3 : 5. Their present ages are

(a) 31 and 48 years

(b) 33 and 51 years

(c) 36 and 52 years

(d) 40 and 56 years

**Answer:** (d) 40 and 56 years

Let the present ages of two persons be 5x, 7x

A/Q | 5x - 16 | = | 3 |

7x - 16 | 5 |

⇒ 25x - 80 = 21x - 48

⇒ 4x = 32

⇒ x = 8

∴ Present ages are 40 and 56 years

Q19. Maidul was thrice as old as Zahidul 3 years back. Maidul will be 5/3 times as old as Zahidul 3 years hence. How old is Zahidul today ?

(a) 3 years

(b) 4 years

(c) 5 years

(d) 6 years

**Answer:** (d) 6 years

3 years back

Zahidul's age be x years

∴ Maidul's age be 3x years

Zahidul's present age = x+3

Maidul's present age = 3x+3

Zahidul's age after 3 years = x + 3 + 3 = x + 6

Maidul's age after 3 years = 3x + 3 + 3 = 3x + 6

A/Q 3x + 6 = (x+6) X 5/3

⇒ 9x + 18 = 5x + 30

⇒ 4x = 12

⇒ x = 3

Zahidul's present age = 3+3 = 6 years

Q20. Sunil's age after 11 years will be 5 times his age 5 years back. What is the present age of Sunil ?

(a) 8 years

(b) 9 years

(c) 10 years

(d) 11 years

**Answer:** (b) 9 years

Let, the present age of Sunil's be x years

5 years back Sunil's age = x - 5

A/Q x + 11 = 5 (x-5)

⇒ x + 11 = 5x - 25

⇒ 4x = 36

⇒ x = 9 years

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