Question

The sum if the digits of a two digit number is 9. Number formed by interchanging the digits is 45 more than the original number. Find the original number and check the solution.​

Answer 1

Answer:

If you call the first digit of the original question “x” and the second digit “y”, the difference between 10y+x and 10x+y is 45. 10y+x-10x-y = 9y-9x = 45, so y-x = 5

pls mark brainliest if you got help

We already know that x + y = 9, and if y-x = 5, 2y = 14, so y = 7, and x = 2.

27 is the answer

Answer 2

Answer:

The required two - digit number is 27.

Step-by-step-explanation:

Let the unit digit at tens place be x.

And the digit at the units place be y.

$\therefore\red{\sf\:The\:original\:number\:=\:10x\:+\:y}\\\\\therefore\pink{\sf\:The\:number\:obtained\:by\:interchanging\:the\:digits\:=\:10y\:+\:x}$

Now, from the first condition,

$\sf\:Sum\:of\:digits\:=\:9\\\\\therefore\boxed{\sf\:x\:+\:y\:=\:9}\:\:\:\:-\:-\:-\:(\:1\:)$

Now, from the second condition,

$\sf\:Original\:number\:+\:45\:=\:The\:number\:obtained\:by\:interchanging\:the\:digits\\\\\therefore\sf\:10x\:+\:y\:+\:45\:=\:10y\:+\:x\\\\\implies\sf\:10x\:-\:x\:+\:y\:-\:10y\:=\:-\:45\\\\\implies\sf\:9x\:-\:9y\:=\:-\:45\\\\\implies\boxed{\sf\:x\:-\:y\:=\:-\:5}\:\:\:[\sf\:Dividing\:both\:sides\:by\:9\:]\:\:-\:-\:(\:2\:)$

Now,

$\sf\:x\:+\:\cancel{y}\:=\:9\:\:\:-\:-\:-\:(\:1\:)\\\\\sf\:x\:-\:\cancel{y}\:=\:-\:5\:\:\:-\:-\:(\:2\:)\\\\\implies\sf\:2x\:=\:4\\\\\implies\sf\:x\:=\:\frac{\cancel4}{\cancel2}\\\\\implies\boxed{\red{\sf\:x\:=\:2}}$

Now, by substituting this value of $\sf\:x\:=\:2$ in equation ( 1 ), we get,

$\sf\:x\:+\:y\:=\:9\:\:-\:-(\:1\:)\\\\\implies\sf\:2\:+\:y\:=\:9\\\\\implies\sf\:y\:=\:9\:-\:2\\\\\implies\boxed{\red{\sf\:y\:=\:7}}$

Now,

$\therefore\pink{\sf\:The\:original\:number\:=\:10x\:+\:y}\\\\\implies\sf\:10\:\times\:2\:+\:7\\\\\implies\sf\:20\:+\:7\\\\\implies\boxed{\red{\sf\:27}}\\\\\orange{\sf\:The\:number\:obtained\:by\:interchanging\:the\:digits\:=\:10y\:+\:x}\\\\\implies\sf\:10\:\times\:7\:+\:2\\\\\implies\sf\:70\:+\:2\\\\\implies\boxed{\pink{\sf\:72}}$

Verification:

$\sf\:x\:+\:y\:=\:9\:\:\:-\:-\:(\:1\:)\\\\\implies\sf\:2\:+\:7\\\\\implies\red{\sf\:9\:=\:9}\\\\\boxed{\red{\sf\:LHS\:=\:RHS}}\\\\\sf\:10x\:+\:y\:+\:45\:=\:10y\:+\:x\:\:\:-\:-\:(\:2\:)\\\\\implies\sf\:27\:+\:45\\\\\implies\pink{\sf\:72\:=\:72}\\\\\boxed{\pink{\sf \:LHS\:=\:RHS}}$

Hence verified!