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    A shopkeeper sold a book at a loss of 14%. If the selling price had been increased by Rs. 100, there would have been a gain of 6%. What was the cost p
    Question

    A shopkeeper sold a book at a loss of 14%. If the selling price had been increased by Rs. 100, there would have been a gain of 6%. What was the cost price of the book?

    A.

    Rs. 650

    B.

    Rs. 500

    C.

    Rs. 970

    D.

    Rs. 450

    Correct option is B

    Given:
    Initial loss percentage = 14%
    If the selling price is increased by Rs. 100, the profit percentage becomes 6%.
    Formula Used:

    Loss % = CPSPCP×100\frac{ CP – SP}{CP} \times 100​​

    Profit % = SPCPCP×100\frac{SP – CP} {CP} \times 100​​

    Solution:
    Let the cost price (CP) of the book be x.
    Selling price at a loss of 14%:
    SP (initial)=x×(114100)=0.86x\text{SP (initial)} = x \times (1 - \frac{14}{100}) = 0.86x​​
    Selling price at a gain of 6%:
    SP (increased)=x×(1+6100)=1.06x\text{SP (increased)} = x \times (1 + \frac{6}{100}) = 1.06x​​
    Given that increasing the SP by Rs. 100 changes the loss to a gain:
    0.86x + 100 = 1.06x
    1.06x - 0.86x = 100
    0.20x = 100
    x = 1000.20\frac{100}{0.20} = 500
    Thus, the cost price of the book is Rs. 500.

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