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Sum of the digits of a two digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 62.Find the numbers . help me :/ |
| Answer» QUESTION :Sum of the digits of a two digit number is 9 when we interchange the digits it is found that the resulting number is greater than the original number by 63 .Find the numbers .Given :Sum of the digits of a two digit number = 9 When interchanging the digits the resulting number is greater than original number by 63.To find :Original number and interchanged numberSolution :Let the digit at one's place be x and digit at ten's place be y∴ Original number = x + 10yNow according to first condition,⇒ x + y = 9 ⇒ x = 9 - y .............. (i) Now if we interchange digits, then interchanged number :∴ Interchanged number = y + 10xNow according to 2ND condition,⇒ y + 10X = x + 10y + 63⇒ y + 10x - x - 10y = 63⇒ 9X - 9y = 63⇒ 9(x - y) = 63⇒ 9(9 - y - y) = 63⇒ 9(9 - 2y) = 63⇒ 81 - 18y = 63⇒ -18y = 63 - 81⇒ y = -18/-18⇒ y = 1Now putting value in (i) :⇒ x = 9 - 1⇒ x = 8∴ Original number = x + 10y = 8 + 10(1) = 8 + 10 = 18∴ Interchanged number = y + 10x = 1 + 10(8) = 1 + 80 = 81Therefore,Original number is 18 and interchanged number is 81. | |