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    Question

    In the question, two quantities I and II are given. You

    have to solve both the quantities to establish the correct relation between Quantity-I and Quantity-II and choose the correct option. Quantity I: X and Y entered into a partnership by investing in the ratio of 7:4 respectively. Y remained in the business for 5 months more than X. If X received Rs. 2100 out of a total profit of Rs. 4900, find the duration for which Y invested his capital. Quantity II: 9 months
    A Quantity-I > Quantity-II Correct Answer Incorrect Answer
    B Quantity-I < Quantity-II Correct Answer Incorrect Answer
    C Quantity-I ≤ Quantity-II Correct Answer Incorrect Answer
    D Quantity-I ≥ Quantity-II Correct Answer Incorrect Answer
    E Quantity-I = Quantity-II or No relation Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let X invested for x months, so Y invested for (x + 5) months.

    Capital ratio = 7:4

    Using the profit ratio:

    Image

    Now, cross-multiply:

    7x×4=4(x+5)×3⇒28x=12x+60⇒16x=60⇒x=3.75

    Time for which Y invested = x+5=3.75+5=8.75 months

    Quantity I = 8.75 months

    Quantity II = 9 months

    So, Quantity I < Quantity II

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