Question

The two digit numbers differ by 3. if you inter change the digit and add with original you will get 99. What is the two digit number?​

Answer 1

Answer:

99 number is different two digit number

Answer 2

Solution :

Let the ten's place digit be r & one's place digit be m;

$\boxed{\bf{Original\:number=10r+m}}}}\\\boxed{\bf{Reversed\:number=10m+r}}}}$

A/q

$\longrightarrow\sf{r-m=3}\\\\\longrightarrow\sf{r=3+m.....................(1)}$

&

$\longrightarrow\sf{10m+r +10r+m=99}\\\\\longrightarrow\sf{11m+11r=99}\\\\ \longrightarrow\sf{11(m+r)=99}\\\\\longrightarrow\sf{m+r=\cancel{99/11}}\\\\\longrightarrow\sf{m+r=9}\\\\\longrightarrow\sf{m+3+m=9\:\:[from(1)]}\\\\\longrightarrow\sf{2m=9-3}\\\\\longrightarrow\sf{2m=6}\\\\\longrightarrow\sf{m=\cancel{6/2}}\\\\\longrightarrow\bf{m=3}$

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

$\longrightarrow\sf{r=3+3}\\\\\longrightarrow\bf{r=6}$

Thus;

$\boxed{\sf{Original\:number=10r+m=[10(6) + 3] = [60+ 3]= \boxed{\bf{63}}}}\\\boxed{\sf{Reversed\:number=10m+r=[10(3) + 6] = [30 + 6]= \boxed{\bf{36}}}}$