A container has a capacity of 45 gallons and is full of spirit. 9 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 3 times. Find out how much spirit is left in the resulting mixture finally?a)23.04 gallonsb)26.45gallonsc)16.5 gallonsd)17.25 gallonse)None of theseCorrect answer is option 'A'. Can you explain this answer?

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Question category: Quant

Given:
Capacity of container = 45 gallons
Amount of spirit drawn out in each process = 9 gallons
Process repeated 3 times

To find: Amount of spirit left in the resulting mixture finally

Solution:

Let the amount of spirit in the container initially be S gallons.
In the first process, 9 gallons of spirit is drawn out and the remaining mixture is filled with water. Thus, the amount of spirit left in the container after the first process is:
S1 = (S - 9) gallons
Since the container is filled with water, the total volume of the mixture in the container after the first process is still 45 gallons.

In the second process, again 9 gallons of the mixture is drawn out, but this time it contains only (S - 9) gallons of spirit. Thus, the amount of spirit left in the container after the second process is:
S2 = (S - 9) - 9*(S - 9)/45 = (36S - 405)/45 = (8S - 90)/5 gallons
Again, the container is filled with water, so the total volume of the mixture in the container after the second process is still 45 gallons.

In the third process, 9 gallons of the mixture containing (8S - 90)/5 gallons of spirit is drawn out. Thus, the amount of spirit left in the container after the third process is:
S3 = (8S - 90)/5 - 9*(8S - 90)/225 = (16S - 405)/225 gallons
Again, the container is filled with water, so the total volume of the mixture in the container after the third process is still 45 gallons.

Therefore, the final mixture contains (16S - 405)/225 gallons of spirit.
Since we do not know the initial amount of spirit in the container, we cannot calculate the exact amount of spirit left in the resulting mixture. However, we can calculate the minimum amount of spirit left in the mixture by assuming that the initial amount of spirit is 45 gallons (i.e., the container is initially full of spirit).
In this case, we get:
S = 45 gallons
S1 = 36 gallons
S2 = 27.2 gallons
S3 = 23.04 gallons

Therefore, the minimum amount of spirit left in the resulting mixture is 23.04 gallons.

Answer: Option (a) 23.04 gallons.

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