Super Math Riddles l Age Puzzles With Answers l Popular Age Problem

Can you solve this Riddles?

 Riddle 1: The sum of the ages of A and B is 30 years, and after 5 years A will be 3 times as old as B. Find their present ages? 

Answer : 

Suppose A's age = x years. 

                B's age = (30-x) years. 

 After 5 years A's age will be

 X + 5 years. 

After 5 years B's age will be

(30-x)+5=35-x years.

 ; X+5=3(35-x)

Or x+5=105-3x

Or x+3x=105-5

  4x=100

    x=25

A's present age = 25 years.

And B's =5 years. 

Riddle 2: One hundred men are distributed into two groups. Five-eighths of the larger group includes 17 more men than the smaller group. How many men are in the larger group? 

Answer : 

Total No. Of men = 100

 Suppose No. of men in the larger group  =x

Hence ;  ;  ;  smaller ; 

= 100-x 

Hence 5/8(x)-17=100-x

or 5x/8+x=100+17=117

or 13x=117×8

 x=72

Hence No. in the larger group

 =72

No. in the smaller group =28 Ans.

Riddle 3: Two men purchased an estate for $9000. A could pay the whole if B gave him half his capital, while B could pay the whole if A gave him one third of his capital, find how much money each of them had. 

Answer : 

Suppose A had $ x

And         B had $ y

Hence x+y/2 = 9000  (i)

             y+x/3 = 9000  (ii)

2  (i) gives 2x+y = 18000  (A)

3  (ii) gives x+3y = 27000  (B)

2  (B) gives 2x+6y= 54000  (C)

                     2x+  y = 18000  (A)

By subtraction  5y = 36000

                                y =  7200

   Putting y = 720 in (i) x=5400 Ans.

Riddle 4: A father is twice the age of his two sons. The age of the elder son is double that of the younger one. Nine years hence the father's age will be thrice that of the younger one. State the ages of the father and his two sons.

Answer: 

Suppose the percent age of the younger son = x years.

Suppose the percent age of the elder son = 2x years. 

Suppose the percent age of father = 2(x+2x) = 6x years.

9 years hence father's age =6x+9 years. 

;  ;  ; age of younger son = (x+9) years.

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

             3x =18 or x=6

Hence age younger son = 6 years.

                      elder son     = 12 years.

                       father          = 36 years.

Riddle 5: Father says to his son, " seven years ago I was seven times as old as you were. Three years hence, my age will be thrice that of yours". What are their precent ages? 

Answer : 

Suppose 7 years ago son was x years old. 

;  ;  ; Father = 7x

Precent age of son = x+7 years.

Precent age of father = 7x+7 ;

3 years hence son will be

  x+7+3=x+10 years. Old

3 years hence father will be

7x+7+3=7x+10;

Hence 7x+10=3(x+10)

             7x-3x=30-10 or

             4x = 20  hence x = 5

Present age of the son is 

               x+7 = 12 years.

Present age of the father

                7x+7 = 42 years. Ans.