Question

The sum of digits in a two digit number formed by two digits from 1 to 9 is 8. If 9 is added to a number then both the digits become equal. find the number.​

Answer 1

Explanation:

Here we need to set a system of two linear equations in two variables. So:

• The sum of digits in a two digit number formed by two digits from 1 to 9 is 8:

Let $x \ and \ y$ be those digits, then:

$x+y=8 \ \ldots eq1$

• If 9 is added to a number then both the digits become equal. find the number:

$10x+y+9 \ldots expression \ 1$

But from eq 1:

$y=8-x$

Substituting y into the expression 1:

$10x+(8-x)+9=9x+17$

The x-value will be found by hit and trial, so:

• Let x = 1:

$9x + 17 = 9(1)+17 = 26$

We have to reject this solution because digits are different.

• Let x = 2:

$9x + 17 = 9(2)+17 = 35$

We have to reject this solution because digits are different.

• Let x = 3:

$9x + 17 = 9(3)+17 = 44$

Then this is a two digit number formed by two equal digits.

Finally, the number is:

44