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    Question

    There are three numbers 'x', 'y' and 'z' (x < y < z) such that 'y' is equal to the average of 'x' and 'z'. 40% of 'z' is equal to 'x' and the difference between 'y' and 'z' is 15. Find the sum of all three numbers.

    A 299 Correct Answer Incorrect Answer
    B 120 Correct Answer Incorrect Answer
    C 110 Correct Answer Incorrect Answer
    D 105 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ, 'y' = (1/2) × (x + z) Or, 2y = x + z And, 0.4z = 'x' Or, z = 5:2 Let 'z' = '5b' and 'x' = '2b' So, 2y = 2b + 5b Or, 'y' = (7b/2) Now, z - y = 15 Or, 5b - (7b/2) = 15 Or, (3b/2) = 15 Or, 'b' = 10 Required sum = 2b + {(7/2) × 10} + (5 × 10) = 20 + 35 + 50 = 105

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