Q. Two boys are playing on a ground. Both the boys are less than 10 years old. Age of the younger boy is equal to the cube root of the product of the age of the two boys. If we place the digit representing the age of the younger boy to the left of the digit representing the age of the elder boy, we get the age of the father of the younger boy. Similarly, we place the digit representing the age of the elder boy to the left of the digit representing the age of the younger boy and divide the figure by 2, we get the age of the mother of the younger boy. The mother of the younger boy is younger than his father by 3 years. Then, what is the age of the younger boy.

Option
a) 3
b) 4
c) 2
d) None of these.

• 2 years
  ages are 4 years and 2 years.
  age of father = 24 years
  age of mother of younger boy = 42/2=21 yrs which is 3 less than 24 years.
• 11 years agoHelpfull: Yes(4) No(0)
• Assume A is elder and B is younger, on 1st condition --- B=cuberoot(A*B) thus cubing on both sides we get B^3=A*B and hence A=B^2. 2nd condition is about placing digits in particular order to get younger boy mother and father age. if we place there ages in "BA" order,the number we get is 10B+A which is Fathers age. and in order "AB/2",the number is (10A+B)/2 which is Mothers age.
  
  
  10B+A=F & 10A+B=2M and it has been given that F=M+3. and hence
  
  10B+A=M+3. and by first condition A=B^2. On proper substitution we get
  
  10B^2 +B = 2(10B + B^2 - 3) which is 8B^2 - 19B+6=0. we get 2 roots but valid root will be 2. and hence
  
  B's age is 2. A's age is 4.
  
• 10 years agoHelpfull: Yes(1) No(0)
• they given that the age of younger boy mother is 3 years younger than age of younger boy father...so find the equation of younger boy father in terms of younger boy mother..also given that if we put the age of younger boy to the left of the age of elder boy we get the age of younger boy's father age...so substitute the age of younger boys father in terms of younger boy mother which we found previously.... also given that if we put the age of elder boy to the left of the age of younger boy we get the age of younger boy mother age ....so equate the two equations of younger boy mothers age....and we get the expression as YE=((EY)/2)+3.... if we solve this equation we get 2YE=EY+6...
  where E-age of elder boy...Y-age of younger boy....if we solve for younger boys age...using above expression we get....the age of elder boy is 4years old and age of younger boy is 2years old ... so option is (3)....this is my answer am not sure... if any mistake...please make correction..
• 11 years agoHelpfull: Yes(0) No(0)
• c
  Ans: Age of the younger boy is 2 and elder boy is 4
• 10 years agoHelpfull: Yes(0) No(0)