On January 1st, 2023, a person saved Rs 1. On January 2nd, 2023, he saved Rs. 2 more than that on the…
On January 1st, 2023, a person saved Rs 1. On January 2nd, 2023, he saved Rs. 2 more than that on the previous day. On January 3rd, 2023, he saved Rs. 2 more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well a perfect cube?
7th January, 2023
8th January, 2023
9th January, 2023
Not possible
Solution
Daily savings form the odd-number series 1, 3, 5, 7, ... The total by 8th January is $1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 = 64$. Since $64 = 8^2 = 4^3$, it is both a perfect square and a perfect cube. Hence the date is 8th January, 2023.