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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: Bhanu and Bala together can complete a task in 30 days, while Bala and Bimal can finish the same task in 24 days. If Bala and Bimal have the same efficiency, then in how many days can Bhanu alone complete 40% of the task? Quantity II: R and S alone can complete the task in 50 and 75 days respectively. How many days will it take if both work together?
    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 the total work be LCM (30, 24) = 120 units

    Work done by Bhanu and Bala per day = 120 ÷ 30 = 4 units

    Work done by Bala and Bimal per day = 120 ÷ 24 = 5 units

    Since efficiency of Bala and Bimal is the same,

    Work done by Bala per day = 5 ÷ 2 = 2.5 units

    Work done by Bimal per day = 2.5 units

    Work done by Bhanu per day = 4 – 2.5 = 1.5 units

    Now, Bhanu needs to complete 40% of 120 = 48 units

    Time = 48 ÷ 1.5 = 32 days

    Quantity II:

    Time taken = (50 × 75)/(50 + 75) = 3750/125 = 30 days

    So, Quantity-I > Quantity-II

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