2019 · Q6
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 a previous year and cube of a number in the next year?
Elementary MathematicsNumber System
- A7 years
- B12 years
- C14 years
- D21 years
Explanation
Let her age be m: m−4 = k^3 and m+4 = n^2 with k ≠ 1, so n^2 − k^3 = 8. k = 2 gives n^2 = 16, so she is 12 now. Waiting w years, need age+w−1 a square and age+w+1 a cube: l^3 − j^2 = 2 gives l = 3, j = 5 (27−25 = 2), so 12+w−1 = 25 and w = 14 years.