Problems on Ages - Solved Examples Set 02

Problems with Solutions: Set 02

Question No. 01
Ratio of A's age to B's age is equal to 4:3. A will be 26 years old after 6 years. How old is B now?

Solution:
A's present age = (26 - 6) = 20 years
B's present age = 20 × (3/4) = 15 years

Question No. 02
The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

Solution:
Let the present ages of son and father be ‘x’ and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
       => 54 - x = 5x - 30
       => 6x = 84
       => x = 14.
Son's age after 6 years = (x+ 6) = 20 years.

Question No. 03
 At present, the ratio between the ages of ‘A’ and ‘B’ is 4 : 3. After 6 years, A's age will be 26 years. What is the age of ‘B’ at present?

Solution:
Let the present ages of ‘A’ and ‘B’ be ‘4x’ years and ‘3x’ years respectively.
Then, 4x + 6 = 26
       => 4x = 20
       => x = 5.
B's age = 3x = 15 years.

Question No. 04
A is younger than B by 7 years. If their ages are in the respective ratio of 7 : 9, how old is A?

Solution:
Let B's age be ‘x’ years.
Then, A's age = (x - 7) years.
             => (x - 7)/x =7/9
             => (9x - 63) = 7x
             => 2x = 63
             => x = 31.5
Hence, A's age =(x - 7) = 24.5 years.

Question No. 05
The ratio of the ages of father and son at present is 6:1. After 5 years the ratio will become 7:2. The present age of the son is:

Solution:
Let their present ages be 6x and x years respectively.
Then 6x + 5)/(x + 5) = 7/2 = 2 (6x + 5) = 7 (x + 5) or, x=5
Therefore, Present age of the son = 5 years.

Question No. 06
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Solution:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x - 8) + (7x - 8) + (9x - 8) = 56
        => 20x = 80
        => x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.

Question No. 07
Alisha'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?

Solution:
Mother's age when Alisha's brother was born = 36 years.
Father's age when Alisha's brother was born = (38 + 4) years = 42 years.
Required difference = (42 - 36) years = 6 years.

Question No. 08
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?

Solution:
Let, the mother's present age be ‘x’ years.
Then, the person's present age = [(2/5) x] years.
       Therefore,   [(2/5)(x + 8)] = [(1/2)(x + 8)]
                    => 2(2x + 40) = 5(x + 8)
                    =>x = 40.
Hence, at present mother’s age is 40 years.

Question No. 09
Three years ago the average age of ‘A’ and ‘B’ was 18 years. With ‘C’ joining them now, the average becomes 22 years. How old is C now?

Solution:
(A+B)'s total present age = (2 x 18+3+3) = 42 years ----- (1)
(A+B+C)'s total present age = 22 x 3 = 66 years -------- (2)
Substituting Eq. (2) from (1), C's age = 66-42 = 24 years

Question No. 10
The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:

Solution:
Let the ages of father and son 10 years ago be ‘3x’ and ‘x’ years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
          => 3x + 20 = 2x + 40
          => x = 20.

Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

Problems on Ages:
Formula:                Problems on Ages Formulas
Solved Examples:  Solved Examples: Set 01     Solved Examples: Set 02
Practice Test:         Practice Test: 01     Practice Test: 02
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