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Two Cask Mixture Muse (Posted on 2022-09-08)

A cask P is filled with 50 liters of water, and cask Q with 40 liters of acid. Precisely x liters are drawn from each cask and then, mixed and replaced. The same operation is then repeated.

Accordingly, the foregoing operation is performed precisely 2 times.

After the conclusion of the 2nd operation, precisely 8.875 liters of acid remain in cask P.

Determine the value of x.

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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Solution

| Comment 1 of 2

x = 10 liters

Notation: (a,b) = litres of (h20, acid) in each cask, respectively.

Initial State: P=50,0 Q=0,40

Remove 10 liters from each P=40,0 Q=30,0

Mix and refill P=45,5 Q=5,35

Remove 10 liters from each P=36,4 Q=3.75, 26.25

At this point, the new 20 liter mixture (call it M) is M=10.25, 9.75

Refill P=(36+10.25/2, 4+9.75/2)=41.125, 8.875 (=50 checks out)

Q=(3.75+10.25/2, 26.25+9.75/2)= 8.875, 31.125 (=40, checks out)

Note that the amount of acid in P must equal the amount of water in Q after each mix and refill, which is another double check.

Posted by Kenny M on 2022-09-08 07:39:45

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