Question

In a two digit number, the sum of the digits is 12. The digits interchange
their places if 54 is added to the number ,find the number .

Answer 1

Answer:

33

Step-by-step explanation:

12/2 = 6

12 + 54 = 66

66/2 = 33

pls subscribe KV Talent

Answer 2

$\large\underline{\sf{Solution-}}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Let-\begin{cases} &\sf{digits \: at \: ones \: place \: be \: x} \\ &\sf{digit \: at \: tens \: place \: be \: y} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:So-\begin{cases} &\sf{number \: formed \: be \: 10y + x} \\ &\sf{reverse \: number \: be \:10x + y} \end{cases}\end{gathered}\end{gathered}$

According to statement

Sum of digits of 2 digit number = 12

$\rm :\longmapsto\:x + y = 12 - - - (1)$

According to statement,

The digits are reversed if 54 is added to the number.

$\rm :\longmapsto\:10y + x + 54 = 10x + y$

$\rm :\longmapsto\:10x + y - 10y - x = 54$

$\rm :\longmapsto\:9x - 9y = 54$

$\rm :\longmapsto\:x - y = 6 - - - (2)$

On adding equation (1) and equation (2), we get

$\rm :\longmapsto\:2x = 18$

$\bf\implies \:x = 9 - - - (3)$

On substituting x = 9 in equation (1), we get

$\rm :\longmapsto\:9 + y = 12$

$\bf\implies \:\:y = 3$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Hence-\begin{cases} &\sf{digits \: at \: ones \: place \: = \: 9} \\ &\sf{digit \: at \: tens \: place \: = \: 3} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:So-\begin{cases} &\sf{number \: formed \: = \: 10 \times 3 + 9 = 39} \\ &\sf{reverse \: number \: = \:10 \times 9 + 3 = 93} \end{cases}\end{gathered}\end{gathered}$

Hence,

• Two digit number is 39

Aliter Method

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:Let-\begin{cases} &\sf{digits \: at \: ones \: place \: be \: x} \\ &\sf{digit \: at \: tens \: place \: be \: 12 - x} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf\: \rm :\longmapsto\:So-\begin{cases} &\sf{number \: formed = 10(12 - x) + x = 120 - 9x} \\ &\sf{reverse \: number \: = \:10x + 12 - x = 9x + 12} \end{cases}\end{gathered}\end{gathered}$

According to statement,

The digits are interchange, when 54 is added to the number.

$\rm :\longmapsto\:120 - 9x + 54 = 9x + 12$

$\rm :\longmapsto\:174 - 9x = 9x + 12$

$\rm :\longmapsto\:9x + 9x = 174 - 12$

$\rm :\longmapsto\:18x = 162$

$\bf\implies \:x = 9$

$\begin{gathered}\begin{gathered}\bf \: So - \begin{cases} &\sf{number \: formed = 120 - 9x = 120 - 81 = 39}\end{cases}\end{gathered}\end{gathered}$