# Problems on Ages

Q1. The sum of the ages of A and B is 63 years. After 6
years, the age of B will be four times that of the A. What
is the age of B ?

(a) 46 Years

(b) 50 Years

(c) 53 Years

(d) 60 Years

**Answer:**(c) 53 Years

Let the Present Age of A is x years

So the Present Age of B = (63 - x) Years

After 6 Years,

(63 - x) + 6 = 4(x + 6)

69 - x = 4x + 24

5x = 45

x = 9

So the present age of B is = (63 - x)= 63 - 9= 53 Years

Q2. Rohit is twice as old as Rakesh was two years ago. If
the difference between their ages be 4 years, how old is
Rohit today ?

(a) 5 Years

(b) 8 Years

(c) 10 Years

(d) 12 Years

**Answer:**(d) 12 Years

Let the age of Rakesh two year ago is x years

So the Present Age of Rohit is 2x Years and Present age of Rakesh is (x + 2) Years

So,

2x - (x + 2) = 4

2x - x - 2 = 4

x = 6

So the present age of Rohit is = 2 X 6 = 12 Years

Q3. The sum of the ages of 4 children born at the
intervals of 3 years each is 42 years. What is the age of
the youngest child ?

(a) 4 Years

(b) 6 Years

(c) 9 Years

(d) 10 Years

**Answer:**(b) 6 Years

Let the age of the youngest child is x years. So the age of other childs will be (x + 3), (x + 6) and (x + 9)

x + (x + 3) + (x + 6) + (x + 9) = 42

4x = 42 - 18

x = 6

So the age of the youngest child is = 6 Years

Q4. 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 years, then how
old is B ?

(a) 9 Years

(b) 10 Years

(c) 7 Years

(d) 8 Years

**Answer:**(b) 10 Years

Let the age of C be x years, then the age of B = 2x and age of A = 2x + 2

Then, x + 2x + 2x + 2 = 27

5x = 25

x = 5

So the age of the B is = 2x = 2 X 5 = 10 Years

Q5. The sum of the present ages of a father and his son
is 60 years. Six year ago, father's age was five times the
age of the son. After 6 years, son's age will be ?

(a) 12 Years

(b) 16 Years

(c) 20 Years

(d) 24 Years

**Answer:**(c) 20 Years

Let the present age of son is x, so the age of father will be (60 - x)

Then, six years ago

(60 - x) -6 = 5(x - 6)

6x = 84

x = 14

So the age of son after 6 years = (x + 6) = 14 + 6 = 20 Years

Q6. The difference between the ages of two persons is 15
years. Ten years ago, the elder one was twice as old as
the young one. The present age of the elader person is ?

(a) 35 Years

(b) 36 Years

(c) 30 Years

(d) 25 Years

**Answer:**(a) 35 Years

Let the Present Age of younger one is x years

So the Present Age of elder one is (x + 15) Years

Then, (x + 15) - 10 = 2(x - 10)

x = 25

So the present age of elder person is = (x + 10)= 25 + 10 = 35 Years

Q7. The age of the father is 30 years more than the son's age. Ten years hence, the father's age will become three times the son's age that time. What is the son's present age in years ?

(a) 3 Years

(b) 4 Years

(c) 5 Years

(d) 5 Years

**Answer:**(c) 5 Years

Let the son's present age be X years. Then the father's present age is (X + 30) years

Father's age after 10 years = (X + 40) years

Son's age after 10 years = (X + 10) years

(X + 40) = 3(X +10)

X + 40 = 3X + 30

2X = 10

X = 5

Q8. The ages of Sita and Gita are in the ratio 8:15. After 9 years, the ratio of their ages will be 11:18. What is the difference between their ages ?

(a) 18 years

(b) 21 Years

(c) 22 Years

(d) 25 Years

**Answer:** (b) 21 Years

Let, the ages of Sita and Gita are 8x and 15x

A/Q | 8x + 9 | = | 11 |

15x + 9 | 18 |

⇒ 18 (8x + 9) = 11 (15x + 9)

⇒ 144x + 162 = 165x + 99

⇒ 21x = 63

⇒ x = 3

Difference between their ages = 15X3 - 8X3 = 45 - 24 = 21 years

Q9. The sum of the ages of a father and his son is 50 years now. Four years ago, their ages were in the ratio of 2 : 1. The ratio of the ages of father and son after 10 years will be

(a) 2 : 3

(b) 3 : 2

(c) 4 : 3

(d) 3 : 4

**Answer:** (b) 3 : 2

Let the age of father be x years

∴ the age of son is 50 - x

x - 4 | = | 2 |

50 - x - 4 | 1 |

⇒ | x - 4 | = | 2 |

46 - x |

⇒ x - 4 = 92 - 2x ⇒ 3x = 96 ⇒ x = 32

After 10 years, Father's age = 32 + 10 = 42

Son's age = (50 - 32) + 10 = 28

∴ Ratio = 42 : 28 = 3 : 2

Q10. The ratio of present ages of two brothers is 1 : 2 and 5 years back the ratio was 1 : 3. What will be the ratio of their ages after 10 years ?

(a) 2 : 3

(b) 3 : 4

(c) 4 : 3

(d) 5 : 3

**Answer:** (a) 2 : 3

Let, the ages of two brothers are x and 2x

A/Q | x - 5 | = | 1 |

2x - 5 | 3 |

⇒ 3x - 15 = 2x - 5 ⇒ x = 10

Ratio after 10 years

x + 10 | = | 10 + 10 | = | 20 | = | 2 |

2x + 10 | 2 X 10 + 10 | 30 | 3 |

= 2 : 3