Question

5. A two digit number is such that the sum of its
digits is 4. If 8 is added to the number, its
digers are reversed. Find the number.​

Answer 1

Let the digits be x and y

Then the two-digit number is 10x + y

Given that: 10x + y = 4 (x + y) 

      10x + y = 4x + 4y

       6x = 3y

         y = 2x  --------------- 1

And 10x + y + 18 = 10y + x

Or           9y – 9x = 18 ---------------- 2

Substitute the value of y in eqn 2

18x – 9x = 18

9x = 18

x = 2

Therefore  y = 2x = 2*2 = 4

And the number is 10x + y = 10*2 + 4 = 24

Answer: The two-digit number is 24.

Answer 2

Solution :(Ques.Error)

Let the tens digit number be r

Let the ones digit number be m

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

A/q

$\longrightarrow\tt{10r+m=4(r+m)}\\\\\longrightarrow\tt{10r+m=4r+4m}\\\\\longrightarrow\tt{10r-4r=4m-m}\\\\\longrightarrow\tt{6r=3m}\\\\\longrightarrow\tt{r=3m/6}\\\\\ \longrightarrow\tt{r=m/2.............(1)}$

&

$\longrightarrow\tt{10r+m+18=10m+r}\\\\\longrightarrow\tt{10r-r+m-10m=-18}\\\\\longrightarrow\tt{9r-9m=-18}\\\\\longrightarrow\tt{9(r-m)=-18}\\\\\longrightarrow\tt{r-m=\cancel{-18/9}}\\\\\longrightarrow\tt{r-m=-2}\\\\\longrightarrow\tt{\dfrac{m}{2} -m=-2\:\:[from(1)]}\\\\\longrightarrow\tt{m-2m=-4}\\\\\longrightarrow\tt{-m=-4}\\\\\longrightarrow\bf{m=4}$

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

$\longrightarrow\tt{r=4/2}\\\\\longrightarrow\bf{r=2}$

Thus;

The original number = (10r+m) = 10(2) + 4 = 20 + 4 = 24 .