Question

The sum of the two digits of a 2-digit number is 13. If 9 is subtracted from the number, the digits are reversed. What is the number
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Answer 1

Answer:

Let the ones digit be x

Tens digit is 13-x

Number form = 10(13-x)+x

= 130-10x+x

= 130 -9x

After reversing digits number formed

= 10x + 13-x

9x +13

According to the question

130-9x-9 = 9x+13

121 -9x = 9x+13

121 -13 = 9x+9x

108 = 18x

x= 6

So ones digit is 6

Tens digit is 13-6 = 7

Number = 76

Answer 2

Answer:

76

Explanation:

Let the units digit be x.

Tens digit = 13-x

Original number = 10(13-x)+x = 130-10x+x = 130-9x

After reversing the digits,

Units digit = 13-x

Tens digit = x

New number = 10x+13-x = 9x+13

According to Question,

130-9x-9 = 9x+13

121-13 = 9x+9x

108 = 18x

x = 6

Hence, original number = 76