Aptitude Questions : Ages Set 5

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1. Four years ago, the ratio of the ages of A and B was 5 : 9. 8 years hence the ratio will be 2 : 3 respectively. Find the present age of B?
   A) 25
   B) 20
   C) 40
   D) 60
   E) 24
   
   Answer & Explanation

   C) 40
   Explanation:
   Let 4 years ago A’s age = 5x, B’s age = 9x
   Then 4+8 = 12 years after – (5x+12)/(9x+12) = 2/3
   Solve, x = 4
   B’s present age = 9x+4 = 40
   
   
   
2. Eight years ago, A was 4 times as old as B. After 8 years A will be twice as old as B. What are their ages respectively?
   A) 45, 18
   B) 40, 10
   C) 42, 18
   D) 40, 16
   E) 42, 16
   
   Answer & Explanation

   D) 40, 16
   Explanation:
   Let B’s age 8 yrs ago = x, then A’s age = 4x
   After (8+8) = 16 years:
   (4x+16) = 2 * (x+8)
   Solve, x = 8
   A’s present age = 4x+8 = 40
   B’s present age = x+8 = 16
   
   
   
3. Present age of B is twice that of A. 4 years hence B’s age will be 4 less than twice the age of A. Find the difference in their ages?
   A) 8
   B) 10
   C) 4
   D) 5
   E) Cannot be determined
   
   Answer & Explanation

   E) Cannot be determined
   Explanation:
   Let A’s present age = x, Then B’s present age = 2x
   After 4 years, (2x+4) = 2(x+4) – 4
   0 = 0
   
   
   
4. After 6 years, A’s age will be 3/7th of B’s age. Also 10 years ago, ratio of ages of A and B was 1 : 5. What is A’s present age?
   A) 20
   B) 25
   C) 24
   D) 18
   E) 50
   
   Answer & Explanation

   D) 18
   Explanation:
   Let 10 years ago, A’s age = x, B’s age = 5x
   After (10+6) = 16 years, (x+16) = (3/7) (5x+16)
   Solve, x = 8
   So A’s present age = x+10 = 18
   
   
   
5. B is twice older than C and A is 2 years older than B. If the total of all of their ages is 27, what will be total of the ages of A and C 6 years hence?
   A) 17
   B) 29
   C) 28
   D) 23
   E) 18
   
   Answer & Explanation

   B) 29
   Explanation:
   Let C’s present age = x, then B’s = 2x, and A’s = 2x+2
   Given: x+2x+(2x+2) = 27
   Solve, x = 5
   A’s present age = 2x+2 = 12
   C’s present age = x = 5
   6 years after A+C)’s age = 12+5+6+6 = 29
   
   
   
6. The sum of the present ages of A and B is 50. After 2 years B’s age will be 2 more than C’s age then. If A is younger than C by 4 years, find the age of B 8 years ago.
   A) 20
   B) 40
   C) 28
   D) 26
   E) 22
   
   Answer & Explanation

   A) 20
   Explanation:
   The difference between B and C’s age will remain same
   Let C’s present age = x, so B’s present age = (x+2)
   sum of the present ages of A and B is 50, so A’s age becomes = 50-(x+2) =48-x
   now A is younger than C by 4 years, so 48-x = x – 4
   Solve, x = 26
   B’s present age = x+2 = 28
   Before 8 years, B’s age = 28-8 = 20
   
   
   
7. After 10 years, A’s age will be twice that of B’s age. A’s present age is 6 times that of C. If B’s eighth birthday was celebrated 2 years ago, then what is C’s present age?
   A) 8
   B) 5
   C) 10
   D) 15
   E) 12
   
   Answer & Explanation

   B) 5
   Explanation:
   Let C’s present age = x, then A’s present age = 6x
   Let B’s present age is y.
   Then after 10 years, (6x+10) = 2 (y+10)
   Solve, y = 3x-5 = B’s present age
   B’s eighth birthday was celebrated 2 years ago, so B’s present age = 10, and also 3x-5 = 10
   Solve, x = 5
   
   
8. The ratio of the present ages of A to B is 5 : 3. The ratio of A’s age 4 years ago to B’s age 4 years hence is 1 : 1. What is the ratio of A’s age 4 years hence to B’s age 4 years ago?
   A) 3 : 2
   B) 5 : 2
   C) 3 : 1
   D) 2 : 3
   E) 1 : 3
   
   Answer & Explanation

   C) 3 : 1
   Explanation:
   Let A’s present age = 5x, and B’s = 3x
   Ratio of A’s age 4 years ago to B’s age 4 years hence is 1 : 1. So
   (5x-4)/(3x+4) = 1/1
   Solve x = 4
   So A’s present age = 20, and B’s = 12
   Required ratio = (20+4) : (12-4)
   
   
9. Present age of a father is three times more than his son. 8 years hence, father’s age will be 2 and a half times of his son’s age. After 8 more years, how many times would father be his son’s age?
   A) 3 n half times
   B) 4 times
   C) 1 n half times
   D) 2 times
   E) 3 times
   
   Answer & Explanation

   D) 2 times
   Explanation:
   three times more than
   Let present age of son = x, then of father = x+3x = 4x
   After 8 years, (4x+8) = (5/2) (x+8)
   Solve, x = 8
   Required ratio = (4x+16) : (x+16) = 2 : 1
   
   
   
10. Age of A is three times the sum of ages of B and C. 5 years hence, A’s age will be twice the sum of ages of B and C. The total of their present ages is
    A) 45
    B) 60
    C) 30
    D) Cannot be determined
    E) None of these
    
    Answer & Explanation

    B) 60
    Explanation:
    Let (B+C)’s present age= x
    Then A’s present age = 3x
    After 5 years, (3x+5) = 2*(x+5+5)
    Solve, x = 15
    Sum = x+3x = 4x = 60