Two barrels, A and B, contain unspecified amounts of cider, A containing more than B. From A, pour into B as much cider as B already contains. Then, from B, pour into A as much cider as A now contains. Finally, pour from A into B as much cider as B now has. Both barrels now contain 64 liters of cider. How many liters of cider were in each barrel at the start of the process?

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04-07-2017
Mathematics

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Two barrels, A and B, contain unspecified amounts of cider, A containing more than B. From A, pour into B as much cider as B already contains. Then, from B, pour into A as much cider as A now contains. Finally, pour from A into B as much cider as B now has. Both barrels now contain 64 liters of cider. How many liters of cider were in each barrel at the start of the process?

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ARYANAGARWAL ARYANAGARWAL · Answer 1 · 2017-07-04T20:00:05+02:00

You should go backwards to answer this question
There were 3 steps
Step 1 : Pour from A into B
Step 2: Pour from B into A
Step 3 : Pour again from A into B
And in all three cases the amount of cider gets doubled in the container

Now we go Backwards From step 3
B now contains 64L poured from A. That means previously it was half of 64, i.e.,
B contained half of 64 = 32L
A contained (64+32) = 96L
[We are adding 32L because the amount of cider got decreased in A is the amount of cider got increased in B or vice versa]

Now coming to second step doing same thing, but now it is half of A as B poured into A,
A contained half of 96 = 48L
B contained (32+48) = 80L

Now same thing in Step 1,
B contained half of 80 = 40L
A contained (48+40) = 88L

Therefore the amount of cider contained in the containers at the starting of process is,
A = 88L
B = 40L

[If you want to check you answer, you can put the values of 88 and 40 and go stepwise as written in question to check whether it coming correct or not]