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    If the selling price of a bed is 2-times of initial, then the profit is 11-times of initial. Find the initial profit percentage.
    Question

    If the selling price of a bed is 2-times of initial, then the profit is 11-times of initial. Find the initial profit percentage.

    A.

    92119\frac{2}{11}%​

    B.

    11%

    C.

    111911\frac{1}{9}%​

    D.

    9% 

    Correct option is C

    Given:

    New profit = 11×1 \times ​initial profit.

    Formula Used:

    Profit = SP - CP

    Profit % = ProfitCP×100\dfrac{\text{Profit}}{\text{CP}}\times100​​

    Solution:

    Initial selling price S, cost price C.

    Initial profit = S - C.

    New selling price = 2S

    New profit = 2S - C.

    Given 2S - C = 11(S - C).
    2S - C = 11S - 11C

    -9S + 10C = 0

    S =109 \frac{10}{9}​C
    Initial profit = S-C=(1091)C=19 = \left(\frac{10}{9}-1\right)C = \frac{1}{9}​C.
    Initial profit %=19CC×100=1119\text{Initial profit \%} = \frac{\frac{1}{9}C}{C}\times100 = 11\frac{1}{9}​%

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