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    Question

    ‘P’ and ‘Q’ started a business with investment

    of Rs. 3,000 and Rs. 4,200, respectively. After 8 months, ‘P’ increased his investment by Rs. ‘8y’. After another 8 more months, ‘Q’ decreased his investment by Rs. ‘8y’ and ‘R’ joined the business with Rs. 4,800. At the end of 32 months, the ratio of profit share of ‘P’, ‘R’ and ‘Q’ was 137:100:167, respectively. Which of the following statement(s) is/are true regarding ‘y’? I. Sum of squares of each digit of ‘y’ is 80. II. 12y < √576 × √256 III. The tens digit of ‘y’ is a composite number.
    A Both I and III Correct Answer Incorrect Answer
    B Only II Correct Answer Incorrect Answer
    C Both II and III Correct Answer Incorrect Answer
    D Both I and II Correct Answer Incorrect Answer
    E Only III Correct Answer Incorrect Answer

    Solution

    Ratio of profit share of ‘P’, ‘Q’ and ‘R’, respectively: = [3,000 × 8 + (3,000 + 8y) × 24]:[4,200 × 16 + (4,200 − 8y) × 16]:[4,800 × 16] = (12,000 + 24y) : (16,800 − 16y) : 9,600 So, (12,000 + 24y):9,600 = 137:100 Or, 12,000 + 24y = 13,152 Or, 24y = 1,152 Or, ‘y’ = 48 Statement I:
    Required sum = 4² + 8² = 16 + 64 = 80
    So, statement I is true. Statement II:
    12y = 12 × 48 = 576
    √576 × √256 = 24 × 16 = 384
    Here, 12y > √576 × √256
    So, statement II is false. Statement III:
    Tens digit of ‘y’ = 4, which is a composite number.
    So, statement III is true. Therefore, statements I and III are true.

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