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    Question

    data-end="88">Quantity I:  An article is marked 36% above its cost price and then sold at a discount of ₹168, resulting in a selling price of ₹x. When the same article is marked 28% above its cost price and sold after a discount of ₹144, the final selling price becomes ₹y. Given that the ratio of y to x is 18:19, determine the cost price of the article. Quantity II:  A sum of ₹12,600 is invested for 2 years at an annual compound interest rate of (x - 1)%, yielding ₹2,646 as interest. Find the compound interest earned on investing ₹5,600 for 2 years at an interest rate of (x + 4)%, compounded annually. In the question, two quantities i.e. Quantity I and Quantity II are given. Solve the given quantities to establish the correct relation between them and choose the correct option.
    A Quantity I > Quantity II Correct Answer Incorrect Answer
    B Quantity I < Quantity II Correct Answer Incorrect Answer
    C Quantity I = Quantity II or No relation can be established Correct Answer Incorrect Answer
    D Quantity I ≥ Quantity II Correct Answer Incorrect Answer
    E Quantity I ≤ Quantity II Correct Answer Incorrect Answer

    Solution

    ATQ,

    Quantity I, Let the CP of article be= x Rs. (x × 1.36 - 168)/(x × 1.28 - 144) = 19/18 18 × (1.36x - 168) = 19 × (1.28x - 144) 24.48x - 3024 = 24.32x - 2736 0.16x = 288 x = 1800 Rs. Quantity II, {1 + (x - 1)/100}2- 1 = 2646/12600 {1 + (x - 1)/100}2 = 1 + 0.21 = 1.21 1 + (x - 1)/100 = 1.1 x - 1 = 10 x = 11 x + 4 = 11 + 4 = 15% CI = 5600 × (1.152- 1) = 5600 × 0.3225 = 1806 Rs. Quantity I < Quantity II

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