Question

The sum of the digits of a two digit number is 9. The number formed by reversing the digits is 45 more than the original number find the original number.

Answer 1

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Answer 2

$\fontsize{18}{10}{\textup{\textbf{The number is 27.}}}$

Step-by-step explanation:  Let x be the unit digit and y be the ten's digit of the given two digit number.

Then, the given number is

$n=10\times y+x=10y+x.$

According to the given information, we have

$x+y=9~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\(10x+y)-(10y+x)=45\\\\\Rightarrow 9x-9y=45\\\\\Rightarrow x-y=5\\\\\Rightarrow x=y+5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

Substituting the value of x from equation (ii) in equation (i), we get

$y+5+y=9\\\\\Rightarrow 2y=4\\\\\Rightarrow y=2.$

From equation (ii), we get

$x=2+5=7.$

Therefore, the required two digit number is

$n=10\times2+7=27.$

Thus, the number is 27.