Question

The sum of the digits of a number is 11 and the difference between the number and that formed by reversing the digits is 45. Find the number.​

Answer 1

Answer:

83

Step-by-step explanation:

Let that number be ab, this can also ba [ a is unit digit & b is tens digit ] written as 10a + b.

In question, sum of digits is 11

= > a + b = 11

= > a = 11 - b

When digits are reversed, new number is ba, which can be written as 10b + a.

In question,

= > Original number - new number = 45

= > 10a + b - ( 10b + a ) = 45

= > 10a + b - 10b - a = 45

= > 9a - 9b = 45

= > 9( a - b ) = 45

= > a - b = 5

= > 11 - b - b = 5 { a = 11 - b }

= > 11 - 5 = 2b

= > 6 = 2b

= > 3 = b

Hence, a = 11 - b = 11 - 3 = 8

Number is ab = 83