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    Question

    On reversing its digits, a two-digit number becomes 78

    less than 180% of the original number. Also, the difference between the digits is 2 (tens digit larger). Find the original number.
    A 15 Correct Answer Incorrect Answer
    B 56 Correct Answer Incorrect Answer
    C 20 Correct Answer Incorrect Answer
    D 75 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Let tens = x, units = y. Original = 10x + y; swapped = 10y + x. 10y + x = 1.8(10x + y) тИТ 78 1.8 = 9/5 тЗТ multiply by 5: 50y + 5x = 90x + 9y тИТ 390 тЗТ 85x тИТ 41y = 390 тАж (I) x тИТ y = 2 тАж (II) тЗТ y = x тИТ 2 Substitute in (I): 85x тИТ 41(x тИТ 2) = 390 тЗТ 85x тИТ 41x + 82 = 390 тЗТ 44x = 308 тЗТ x = 7 y = 7 тИТ 2 = 5 Original number = 10├Ч7 + 5 = 75

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