Question

the sum of the digit number is 12 if the digits are interchanged the number is incresed by 18 find the number​

Answer 1

Given :

• The sum of the digit number is 12.
• The digits are interchanged the number is incresed by 18.

To find :

• The number =?

Step-by-step explanation :

Let the tens digit of the required number be x and the units digit be y. Then,

As it is a Given that,

The sum of the digit number is 12.

So,

x + y = 12 .....(i)

So, the new number = (10x + y).

Now,

Number obtained on reversing the digits = (10y+x).

According to the question,

(10y + x) − (10x + y) = 18

9y − 9x = 18

y − x = 2 .....(ii)

On adding (i) and (ii), we get,

x + y + y − x = 12 + 2

2y = 14

y = 7

Therefore, We got the value of, y = 7.

Putting the value of, y = 7 in equation (ii), we get,

y − x = 2

7 - x = 2

-x = 2 - 7

-x = - 5

x = 5.

Therefore, the new number, (10x + y) = 10 × 5 + 7 = 57

Hence, the required number is 57.

Answer 2

Solution :

Let the ten's place digit be r

Let the one's place digit be m

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

A/q

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

&

$\longrightarrow\sf{10m+r=10r+m+18}\\\\\longrightarrow\sf{10m-m+r-10r=18}\\\\\longrightarrow\sf{9m-9r=18}\\\\\longrightarrow\sf{9(m-r)=18}\\\\\longrightarrow\sf{m-r=\cancel{18/9}}\\\\\longrightarrow\sf{m-r=2}\\\\\longrightarrow\sf{m-(12-m)=2\:\:[from(1)]}\\\\\longrightarrow\sf{m-12+m=2}\\\\\longrightarrow\sf{2m=2+12}\\\\\longrightarrow\sf{2m=14}\\\\\longrightarrow\sf{m=\cancel{14/2}}\\\\\longrightarrow\bf{m=7}$

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

$\longrightarrow\sf{r=12-7}\\\\\longrightarrow\bf{r=5}$

Thus;

$\boxed{\sf{The\:number\:=10r+m=[10(5)+7]=[50+7]=\boxed{\bf{57}}}}}$