How long will it take for Akshay's vault to become half-full?

Question:

If Akshay's vault gets filled in 32 days by doubling his money every 25 days, how long would it take his vault to become half-full?

Answer:

If Akshay's vault gets filled in 32 days by doubling his money every 25 days, it would take approximately 22 days for his vault to become half-full.

Akshay has discovered a new scheme where he can double his money every 25 days. If his vault is filled in 32 days, we can calculate how long it would take for his vault to become half-full. Let's break down the calculation:

First, we need to determine how many times Akshay's money doubles within the 32-day period. Since his money doubles every 25 days, we divide 32 by 25. This results in his money doubling once, with a remaining 7-day period.

Next, we calculate the additional amount of money gained during these 7 days using the doubling rate. His money would approximately increase by 1/25 each day. Multiplying this fraction (1/25) by 7 gives us the additional amount of money gained.

Finally, we subtract this additional amount from the total amount in the vault to find the half-full point. By following these calculations, we determine that it would take approximately 22 days for Akshay's vault to become half-full.