Ages of Two Boys and Parents

CAT 2002 Slot 1 · QA · Medium · Number System

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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 father of the younger boy. Similarly, if 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 mother of the younger boy. The mother of the younger boy is younger to his father by 3 years. Then, what is the age of the younger boy?

  1. A.

    3

  2. B.

    4

  3. C.

    2

  4. D.

    None of these

Answer

C

Explanation

Let yy be the age of the younger boy and ee be the age of the elder boy (y,e<10y, e < 10). y=y⋅e3  ⟹  y3=y⋅e  ⟹  e=y2y = \sqrt[3]{y \cdot e} \implies y^3 = y \cdot e \implies e = y^2. Since e<10e < 10, if y=2y = 2, then e=4e = 4. Father's age = 2424. Mother's age = 422=21\frac{42}{2} = 21. Difference between father and mother = 24−21=324 - 21 = 3 years, which matches the problem statement. Thus, the age of the younger boy is 2.

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