Question

Priya's age was cube of an integral number
(different from 1) four years ago and square of
an integral number after four years. How long
should she wait so that her age becomes
square of a number in the previous year and
cube of a number in the next year?​

Answer 1

Answer:

she has to wait for 14 Years

Step-by-step explanation:

Let say Priya age 4 year Ago = X

Current Age = X + 4

Age after 4 Years = X + 4 + 4 = X + 8

X is a cube   & X + 8 is an square

8 & 16 are possible Solution

cube   :  8  ,    27      ,   64  , 125

cube + 8  =  16  ,  35  ,  72  , 133

Squares  4  , 9  , 16  , 25  , 36  , 49 , 64   ,  81 , 90

16 is a square

so X = 8  & X + 8 = 16

so Present age = 12 Years

her age becomes square of a number in the previous year and

cube of a number in the next year

=> Cube = Square + 2

cube = 27  Square = 25

Age = 26 Years

26 - 12 = 14 Years

she has to wait for 14 Years