Question
If the digits of a two-digit number are reversed, the
resulting number is 36 less than twice the original number. If the sum of the digits is 9, what is the original number?Solution
ATQ,
Let the tens digit and unit digit be ‘x’ and ‘y’ respectively. So, the original number = (10x + y) According to the question: 10y + x = 2 × (10x + y) – 36 Or, 10y + x = 20x + 2y – 36 Or, 19x – 8y = 36 ….. (i) Also, x + y = 9 ….. (ii) Multiply equation (ii) by 8: 8x + 8y = 72 ………………….(iii) Add equations (i) and (iii): 27x = 108 x = 4 So, y = 9 – 4 = 5 [from equation (ii)] Original number = 10 × 4 + 5 = 45
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