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    The marked price of an article is Rs. 875. It is sold for Rs. 598.50, after giving three successive discounts of 10%. x% and 20%. What is the sel
    Question

    The marked price of an article is Rs. 875. It is sold for Rs. 598.50, after giving three successive discounts of 10%. x% and 20%. What is the selling price of the article, if it is sold at a single discount of 3x% ?

    A.

    Rs. 743.75

    B.

    Rs. 775

    C.

    Rs. 762.50

    D.

    Rs. 725

    Correct option is A

    Given:

    Marked Price (MP) = Rs. 875

    Selling Price (SP) after three successive discounts = Rs. 598.50

    The successive discounts are 10%, x%, and 20%.

    Formula Used:

    SP = MP ×(1d1100)×(1d2100)×(1d3100)\times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right) \times \left(1 - \frac{d_3}{100}\right)​​

    Solution:

    for the three successive discounts:

    598.50=875×0.90×(1x100)×0.80598.50 = 875 \times 0.90 \times \left(1 - \frac{x}{100}\right) \times 0.80​​

    598.50=875×0.72×(1x100)598.50 = 875 \times 0.72 \times \left(1 - \frac{x}{100}\right)​​

    598.50=630×(1x100)598.50 = 630 \times \left(1 - \frac{x}{100}\right)​​

    598.50630=1x100\frac{598.50}{630} = 1 - \frac{x}{100}​​

    0.95=1x1000.95 = 1 - \frac{x}{100}​​

    x100=0.05\frac{x}{100} = 0.05​​

    x = 5

    Now Selling price for a single discount of 3x = 15%:

    SP = 875×(115100)875 \times \left(1 - \frac{15}{100}\right)​​

    = 875 × 0.85 = Rs. 743.75

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