Question

4. The sum of the digits of a 2-digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.

Answer 1

Answer:

39

Step-by-step explanation:

Their sum is 12.

Their reverse is 93.Then 93-39=54.

Then the orginal number is 39

Answer 2

Solution :

Let the ten's place digit be r

Let the one's place digit be m

$\boxed{\bf{The\:original\:number=10r+m}}}\\\boxed{\bf{The\:reversed\:number=10m+r}}}$

A/q

$\longrightarrow\sf{r+m=12}\\\\\longrightarrow\sf{r=12-m........................(1)}$

&

$\longrightarrow\sf{10m+r=10r+m+54}\\\\\longrightarrow\sf{10m-m+r-10r=54}\\\\\longrightarrow\sf{9m-9r=54}\\\\\longrightarrow\sf{9(m-r)=54}\\\\\longrightarrow\sf{m-r=\cancel{54/9}}\\\\\longrightarrow\sf{m-r=6}\\\\\longrightarrow\sf{m-(12-m)=6\:\:[from(1)]}\\\\\longrightarrow\sf{m-12+m=6}\\\\\longrightarrow\sf{2m-12=6}\\\\\longrightarrow\sf{2m=6+12}\\\\\longrightarrow\sf{2m=18}\\\\\longrightarrow\sf{m=\cancel{18/2}}\\\\\longrightarrow\bf{m=9}$

∴Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=12-9}\\\\\longrightarrow\bf{r=3}$

Thus;

$\boxed{\sf{The\:original\:number\:will\:(10r+m)=[10(3)+9]=[30+9]=\boxed{\bf{39}}}}}$