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The sum of the digits of a two digit number is 7. If the number formed by reversing the digits isless than the original number by 27, find the original number. |
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Answer» Answer: Step-by-step explanation: Suppose the two digit original number is 10x+y. (x is at tens place so multiple by 10 and y is at UNIT place so left as is, you may MULTIPLY it by 1 to get a clear picture but 1y is represented as y only) The sum of digits of original number is 7 →x+y = 7 —equation(1) If 27 is added to original number its digits are interchanged .So, 10x + y +27 =10Y+ x → 9x +27 = 9y → 9(x+3) = 9(y) → x+3 = y — equation(2) Substituting value of y from equation (2) in equation (1) x + x+3 = 7 2x + 3 = 7 2x =4 x= 2 Substituting x= 2 in equation (2) y= 5 So original number is 10 (2) + 5 i.e. 20 +5 → 25. In order to CHECK the answer.. 25 is original number and 52 is the number formed by interchanging the digits. 25 +27 = 52. |
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