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21 April, 09:11

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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  1. 21 April, 11:07
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    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]
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