Question

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. What is the two-digit number? with x only ​

Answer 1

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36

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Let the unit digit be x.

Given,

Unit Digit + Tens digit = 9

Tens Digit = 9-Unit Digit

Tens Digit = 9-x

Original Number = 10(9-x)+x

Original Number = 90-9x

Interchanging the digits,

Units Digit = 9-x

Tens Digit = x

New Number = 10x+9-x

New Number = 9x+9

According to question,

New Number = Old Number + 27

9x+9 = 90-9x + 27

Sending x terms to LHS and constant terms to RHS,

18x = 108

x = 6

Units Digit = 6

Tens Digit = 9-x => 9-6 => 3

Original Number = 36

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