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Question

The 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. What is the two-digit number?

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Solution

Let the digits at tens place and ones place be x and (9−x) respectively.Therefore, original number =10x+(9−x)=9x+9On interchanging the digits, the digits at one's place and tens place will be x and (9−x) respectively.Therefore, new number after interchanging the digits =10(9−x)+x=90−10x+x=90−9xAccording to the given question,New number = Original number +2790−9x=9x+9+2790−9x=9x+36Transposing 9x to R.H.S and 36 to L.H.S, we obtain90−36=18x54=18xDividing both sides by 18, we obtain3=x and 9−x=6Hence, the digits at tens place and one's place of the number are 3 and 6 respectively.Therefore, the two-digit number is 9x+9=9×3+9=36

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