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    If the cost price of six items is equal to the selling price of seven items, then what will be the percentage profit or loss?
    Question

    If the cost price of six items is equal to the selling price of seven items, then what will be the percentage profit or loss?

    A.

    7.14% loss

    B.

    14.28% profit

    C.

    9.09% loss

    D.

    14.28% loss

    Correct option is D

    Given:

    Cost Price of 6 items = Selling Price of 7 items

    Formula Used:

    Profit or Loss %=(SPCPCP)×100\text{Profit or Loss \%} = \left( \frac{\text{SP} - \text{CP}}{\text{CP}} \right) \times 100​​

    Solution:
    Let the Cost Price of 1 item = ₹1
    Then, CP of 6 items = ₹6
    So, SP of 7 items = ₹6 

    SP of 1 item = ₹67\frac{6}{7}​​

    Since SP < CP, it's a loss.

    Loss per item = ₹1 -67=17 ₹\frac{6}{7} = ₹\frac{1}{7}​​

    Loss % =(171)×100=14.28%= \left( \frac{\frac{1}{7}}{ 1} \right) \times 100 = 14.28\%

    Alternate Method:

    6 CP = 7 SP

    CPSP=76\frac{CP}{SP} =\frac 76

    Difference = 7 - 6 =1 (Since, SP < CP, it's a loss)

    Loss % = 17×100=\frac17\times 100= 14.28%​

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