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    Question

    Pipe A and pipe B can fill the empty tank in 20 hours

    and 24 hours, respectively whereas pipe C can empty the full tank ‘x’ hours. Find the value of ‘x’ if pipes A, B and C together can fill the empty tank in 15 hours.
    A 11 Correct Answer Incorrect Answer
    B 13 Correct Answer Incorrect Answer
    C 15 Correct Answer Incorrect Answer
    D 9 Correct Answer Incorrect Answer
    E 12 Correct Answer Incorrect Answer

    Solution

    Let the two numbers be ‘13a’ and ‘13b’
    ATQ;
    13a × 13b = 5070
    So, (a × b) = 30 ……………………. (1)
    Also, 13a + 13b = 143
    So, a + b = 11
    Or, a = (11 – b) …………………... (2)
    Putting value of ‘a’ in equation (1), we have
    (11 – b) × b = 30
    Or, 11b – b 2 = 30
    Or, b 2 – 11b + 30 = 0
    Or, b 2 – 6b – 5b + 30 = 0
    Or, b(b – 6) – 5(b – 6) = 0
    Or, (b – 6)(b – 5) = 0
    So, b = 6 or b = 5
    So, the two numbers are = 13 × 5 = 65 and 13 × 6 = 78
    Required difference = 78 – 65 = 13

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