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    An article was marked at ₹11,500. A discount of 25% was offered, resulting in a profit of15%. What is the cost price of the article?
    Question

    An article was marked at ₹11,500. A discount of 25% was offered, resulting in a profit of15%. What is the cost price of the article?

    A.

    ₹7,700

    B.

    ₹7,500

    C.

    ₹7,400

    D.

    ₹7,200

    Correct option is B

    Given:

    Marked price of the article = ₹11,500

    Discount offered = 25%

    Profit = 15%

    Formula Used:

    Selling Price = Marked Price×(1Discount100) \text{Marked Price} \times (1 - \frac{\text{Discount}}{100})​​

    Profit = Selling PriceCost PriceCost Price×100 \frac{\text{Selling Price} - \text{Cost Price}}{\text{Cost Price}} \times 100​​

    Solution:

    Let the cost price of the article be C

    Selling Price after 25% discount:

    Selling Price = 11,500×(125100)11,500 \times \left(1 - \frac{25}{100}\right)​​

    =11,500×0.75=8,625= 11,500 \times 0.75 = ₹8,625​​​

    Profit = 15%, So

    8,625CC×100=15\frac{8,625 - C}{C} \times 100 = 15​​​

    8,625CC=15100\frac{8,625 - C}{C} = \frac{15}{100}​​

    8,625 - C = 0.15C

    8,625 = 1.15C

    C = 8,6251.15\frac{8,625}{1.15}​ = ₹7,500

    Alternate Solution: 

    MPCP=100+profit%100discount% 11500CP=11575  CP=11500×75115=7500\frac{MP}{CP} = \frac{100+profit\%}{100 - discount\%} \\ \ \\ \frac{11500}{CP}= \frac{115}{75} \\ \ \\ \implies CP = \frac{11500 \times 75}{115} = 7500 ​​

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