Problems on Ages -

A person is 30 years older than his son . After 6 years , the age of that person is four times the age of son that time. What is age of his son after 10 years from now ?
14 years

16 years

18 years

18 years

14.5 years

Option A
Let the age of his son = x
age of person = x + 30
after 6 years ,
4 (x + 6) = x + 30 + 6
3x = 12
x = 4
age of son after 10 years = 10 + 4 = 14 years
The sum of age of A and B is 38 years. After 8 years the age of B is 2 years more than A. What is the age of B before 5 years ?
13 years

14 years

15 years

20 years

18 years

Option C
Let the age of A = x years
age of B = (38 – x) years
after 8 years,
(38 – x + 8) – (x + 8) = 2
x = 18
age of B before 5 years = 38 – x – 5 = 15 years
The age of B is 8 years more than A, the age of C is 11 years less than B and the age of A is 5 years less than D. If the sum of age of A , B ,C and D is 70 years, then find the sum of age of A and B after 2 years ?
40 years

15 years

45 years

38 years

23 years

Option D
Let the age of D = x years
the age of A = (x – 5) years
the age of B = ( x – 5 + 8 ) = x + 3 years
the age of C = (x + 3 – 11) = x – 8 years
total sum of age of A , B ,C and D = 70
x + ( x – 5) + (x +3) + (x -8) = 70
4x – 10 = 70
x = 20 years
The age of A = 20 – 5 = 15 years
The age of B = 20 + 3 = 23 years
sum = 15 + 23 = 38 years
The age of son is one-third of his father. If after 5 years the age of father and son becomes 5 : 2, then find the sum of age of father and son.
50 years

60 years

55 years

45 years

46 years

Option B
Let the age of father = 3x
the age of son = x
after 5 years,
3x + 5/x + 5 = 5/2
6x + 10 = 5x + 25
x = 25
sum = 3x + x = 4x = 4 * 15 = 60 years
The average present age of A , B and C is 30 years and the ratio between the present age of A and C is 4 : 5. If the age of B is 8 years less than the age of C, then what is age of B after 2 years ?
26 years

29 years

23 years

25 years

30 years

Option B
Let the A and C 4x and 5x respectively
the age of B = 5x – 8
total age of A , B and C = 30 * 3 = 90 years
4x + 5x + 5x – 8 = 90
14x = 98
x = 7
the age of B after 2 years = (5x – 8) + 2 = 29 years
The sum of present age of A , B and C is 52 years and the age of A is 3/5th of age of B. If after 11 years the age of B is equal to the three times the present age of C, then find present of C ?
26 years

28 years

30 years

14 years

25 years

Option E
Let the present age of B = 5x
the age of A = 3x
Let the present of C = y years
5x + 11 = 3y
y = 5x + 11/3
3x + 5x + (5x + 11)/3 = 52
9x + 15 x + 5x + 11 = 156
29x = 145
x = 5
the present age of B = 5 * 5 = 25 years
10 years ago P was half of Q in age . At present the ratio of their ages is 3 : 4. Find the sum of their ages after 3 years.
46 years

35 years

62 years

41 years

52 years

Option D
10 years ago , let the age of Q = 2x
and the age of P = x
at present , the age of P = x + 10
the age of Q = 2x + 10
x + 10/2x + 10 = 3/4
6x + 30 = 4x + 40
2x = 10
x = 5
sum of their ages after 3 years = 2x + 13 + x + 13 = 23 + 18 = 41 years
The age of father is 40% more then his son. After 5 years the age of father is 16 years more than the age of son. Find the present age of father.
45

56

42

58

56

Option E
Let age of son = 5x
and father age = 5x * 140/100 = 7x
after 5 years,
(7x + 5) – (5x + 5) = 16
2x = 16
x = 8
the age of father = 7x = 7 * 8 = 56 years
The difference between the present age of A and B is 20 years. After 3 years their ages are in the ratio 9 : 19. Find the present age of B.
40 years

35 years

26 years

14 years

46 years

Option B
Let present age of A = x years
present age of B = x + 20 years
after 3 years, the age of A = x + 3
the age of B = x + 23
x + 3 / x + 23 = 9/19
19x + 57 = 9x + 207
10x = 150
x = 15
the age of B = 15 + 20 = 35 years
The present age of father is 5 times that of his son. After 4 years he will be 4 times that of his son. Find the age of father 3 years ago.
34 years

56 years

42 years

57 years

48 years

Option D
Let the age of son = x years
the age of father = 5x years
After 4 years,
the age of son = x + 4
the age of father = 5x + 4
4 (x + 4) = 5x + 4
4x + 16 = 5x + 4
x = 12 years
the age of father 3 years ago = 5 * 12 – 3 = 57 years

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