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    Question :
    Barbara has boxes in three sizes: large, standard, and small. She puts 11 large boxes on a table. She leaves some of these boxes empty, and in all the other boxes she puts 8 standard boxes. She leaves some of these standard boxes empty, and in all the other standard boxes she puts 8 (empty) small boxes. Now, 102 of all the boxes on the table are empty. How many boxes has Barbara used in total?

    Category Logical & Aptitude Interview Questions
    Rating (0.4) By 1846 users
    Added on 9/18/2009
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    By putting 8 boxes in a box, the total number of empty boxes increases by 8 - 1 = 7. If we call x the number of times that 8 boxes have been put in a box, we know that 11 + 7x = 102. It follows that x=13. In total, 11 + 13 × 8 = 115 boxes have been used.

    It's a tough one.

    Barbara uses 11 big boxed. that's for sure. Out of this, x big boxes are empty and 11-x boxes are filled - each with 8 medium boxes.

    It comes to be that Barbara uses total of (11-x)*8 medium boxes. out of this y medium boxes are empty and (11-x)*8-y medium boxes contain small boxes - each contains 8 small boxes.

    It comes to be that Barbara uses [(11-x)*8-y]*8 small boxes and it's GIVEN that all the small boxes are empty.

    Now build the equation of the empty boxes:
    x + y + [(11-x)*8-y]*8 = 102

    Arranging the equation yields:
    9x + y = 86

    We know that x is between 1 and 10 (including) and y is between 1 and 79 (including) (it's given that there is at least one big and one medium empty boxes).

    Now denote total amounts of big, medium and small boxes:

    TB = 11
    TM = (11-x)*8
    TS = [(11-x)*8-y]*8

    And try to put the numbers in the equation:

    x=1 y=77 TS=24
    x=2 y=68 TS=32
    ... ... ...

    Finally calculate and add up the totals:

    11 + 80 + 24 = 115
    11 + 72 + 32 = 115
    ... ... ... = 115

    As you can see, there might be various combinations of big, medium and small boxes that lead to the correct answer BUT there is only one correct answer.

    Posted by: alex    

    Contact alex Contact alex

    Answer: 16 Boxes

    1. Barbara puts 8 standard boxes in 8 large boxes.
    8 Large Boxes Are Used Here.

    2. Barabara puts 8 small boxes in 8 standard boxes.
    8 Standard Boxes Are Used Here.

    3. Barabara Doesnt Keep Any Thing In Small Box.So, No Small Box Is Used.

    Now Summarize The Used Boxes
    8 Large Boxes + 8 Standard Boxes

    Total Boxes Used: 16

    Abdul Raheem

    Posted by: Abdul Raheem    

    Contact Abdul Raheem Contact Abdul Raheem

    The answer is 602

    11 boxes of large one
    8 boxes of standard one
    8 boxes of small one

    so, each of 11 large boxes may contain 8 boxes of standard one and each 8 standard boxes may contain 8 boxes of small one

    so, 11 * 8 * 8 = 704 boxes total if there we will putting all the boxes none of one is empty..

    now here specify that 102 boxes are empty so,

    704 boxes - 102 empty boxes = 602 boxes which are used by Barbara is the total number of boxes..

    Posted by: Vishal Banker    

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    i think she had a total of 118 Boxes
    she puts 11 Large Boxes on the Table and out of the 11, she fill the 8 with standard Boxes giving 3 empty Boxe large and 8 empty Boxes standard, she then puts 8 small Boxes in the standard boxes that leaves 3 empty large and 8 small.
    so if she has 102 empty boxes, then she has 16 full Boxes, added to the 102 gives u 118 boxes in total

    Posted by: Nannozi Josephine kyolaba    

    Contact Nannozi Josephine kyolaba Contact Nannozi Josephine kyolaba

    firstly, barbara put 11 standard boxes on the table,

    let she filled 'n' large boxes each with '8' standard boxes,

    so we have '11-n' empty large boxes
    and '8n' empty standard boxes.

    now let she filled 'm' standard boxes out of '8n' each with '8' small boxes,so we have '8n-m' empty standard boxes and '8m' empty small boxes.

    so we have total '11-n' empty large boxes, '8n-m' empty standard boxes and 8m empty small boxes.

    ATQ: (11-n)+(8n-m)+8m=102
    => n+m=13

    so total boxes used: '11' large boxes, '8n' standard boxes and 8m small boxes

    so: 11+8n+8m
    11+8*13 since n+m=13

    115 total boxes used by barbara


    Posted by: himanshu singh    

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    there are 11 large boxes.....

    suppose (x) of them filled with std boxes each having 8.....

    so 11-x large boxes are empty.

    Each x large boxes are filled with 8 standard boxes each so total std boxes 8x of which y are empty(suppose).
    and 8x-y are filled with small boxes each 8......

    So now total empty boxes are 8(8x-y)small boxes + y std boxes + 11-x large boxes.
    so simplifying this 11+63x-7y=102
    solving by putting x=2 and y=5

    so 11-2=9 large boxes are empty, y=5 std boxes are empty and 8(8x-y)=88 small boxes are empty

    Posted by: Avadhesh Kumar Maurya    

    Contact Avadhesh Kumar Maurya Contact Avadhesh Kumar Maurya

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