Question

the sum of digits of a two digit number is 17. on reversing its digit the new number in 9 more than the original number. find the number
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Answer 1

Answer:

For the reversal of the digits, base 10, to result in an increment of 9, the digits must differ by one. As it happens, the problem is simplified by the fact that only two single digits sum to 17. 89 is the answer. 8+9=17, if 89 is reversed it becomes 98.

Step-by-step explanation:

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Answer 2

The original number is 89.

• A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. Finding the values of the variables that result in the equality is the first step in solving an equation with variables.
• The unknown variables are also known as the variables for which the equation must be solved, and the unknown variable values that fulfil the equality are known as the equation's solutions. Equations come in two varieties: identities and conditional equations. All possible values of the variables result in an identity. Only certain combinations of the variables' values make a conditional equation true.

Here, according to the given information, we are given that,

The sum of digits of a two digit number is 17.

Let the digits of the number $10x+y$ be x and y.

Then, $x+y = 17...(i)$

On reversing the digits, the new number will be, $10y+x.$

Then, we get,

$10y+x-10x-y = 9.$

Or, $9y-9x=9.$

Or, $y-x=1...(ii)$

Adding equations (i) and (ii), we get,

$2y = 18.$

Or, $y=9.$

Then, we get, $x=17-9.$

Or, $x = 8.$

Hence, the original number is 89.

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