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    Question

    Divide 45 into 4 parts such that if the first is

    increased by 2, the second is decrease by 2, the third is multiplied by 2 and the fourth divided by 2, the result is the same. Find out First part?
    A 8 Correct Answer Incorrect Answer
    B 12 Correct Answer Incorrect Answer
    C 10 Correct Answer Incorrect Answer
    D 20 Correct Answer Incorrect Answer

    Solution

    ATQ, Let the four parts be x, y, z, and w. Denote the common result by k. From the conditions:

    Thus, we can express the parts in terms of k:

    The sum of the parts is:

    Simplifying this gives = 4k + k/2 = 45 Multiply the equation by 2 to get rid of the fraction = 8k+k = 90 Solving for 9k = 90 ⇒ k = 10 Finally, the first part x is = k − 2 = 10−2 = 8 Thus, the first part is 8.

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