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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 (9x) respectively.

Therefore, original number =10x+(9x)=9x+9

On interchanging the digits, the digits at one's place and tens place will be x and (9x) respectively.

Therefore, new number after interchanging the digits =10(9x)+x

=9010x+x

=909x

According to the given question,

New number = Original number +27

909x=9x+9+27

909x=9x+36

Transposing 9x to R.H.S and 36 to L.H.S, we obtain

9036=18x

54=18x

Dividing both sides by 18, we obtain

3=x and 9x=6

Hence, 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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