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3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. Whatis the two-digit number? |
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Answer» The Original Number is 36.Step-by-step explanation:Given :Sum of the Digits = 9The number with interchanged digits is greater than the original number by 27.To Find :The NumberSolution :Orignal Number,Units PLACE as xTens place as 10(9 - x)⇒x + 10(9 - x)⇒ x + 90 - 10x⇒ -9x + 90 ......... [ Original Number ]Number with REVERSED digits, Units Place = (9 - x)Tens Place = 10(x)⇒ 9 - x + 10x⇒ 9 + 9x .......... [ Number with Reversed Digits ]The number with interchanged digits is greater than the original number by 27.⇒ 9x + 9 = ( –9x + 90) + 27⇒ 9x + 9 = - 9x + 117⇒ 9x + 9x = 117 - 9⇒ 18x = 108[⇒ x = 108/18⇒ x = 6Units Place = 6★ Value of 10(9 - x)⇒ 10(9 - 6)⇒ 10(3)⇒ 30The Original Number -⇒ 30 + 6⇒ 36 The Original Number is 36 |
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