Question

the sum of digits of a 2-digit number 11. when we interchange the digits, it is found that the resulting new number is greater than the original number by 9. find the number

Answer 1

Solution -

Let the digit in once place be x

So, the digit in tens place be y

As,

x + y = 11
=> y = 11 - x

Original no. = 10(11 - x) + 1(x)

= 110 - 10x + x

= 110 - 9x

New no. = 10(x) + 1(11 - x)

= 10x + 11 - x

= 9x + 11

According to Question,

New no. - Original no. = 9

=> (9x + 11) - (110 - 9x) = 9

=> 9x + 11 - 110 + 9x = 9

=> 18x - 99 = 9

=> 18x = 9 + 99 = 108

=> x = 108/18 = 6

Therefore,

The original no. = 110 - 9x

= 110 -9(6)

= 110 - 54

= 56

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