Question

addition of digits of 2 digit number is 5 if we interchange the digits the new number is 9 more than original number find original number​

Answer 1

• Let the digit in unit place be 'x' and tens place by 'y'.

Then original will be number is 10y + x.

Given:-

• x + y = 5
• 10x + y = 10y + x + 9

( On interchanging the digits, the number will become 10x + y )

Solution:-

x + y = 5 ...[1]

$\leadsto\rm 10x + y = 10y + x + 9$

$\leadsto\rm 10x-x -10y+y= 9$

$\rightsquigarrow \rm 9x -9y= 9$

Dividing the equation by 9, will imply

$\bullet\qquad\boxed{\rm x -y= 1 } \qquad\qquad ...[2]$

_______________________________

Now we have our simultaneous equations as

$\bullet \ \ \rm x -y=1$

$\quad \rm x+y=5$

Let's solve these simultaneous equations.

Using the method of elimination, eliminating y

Adding the equations will give,

x - y = 1

x + y = 5

+

______

2x = 6

→ x = 6/2

→ x = 3

Substituting the value of x in [2]

x - y = 1

→ 3 - y = 1

→ y = 3 - 1

→ y = 2

_____________

We had our original number as 10y + x

Substituting the values, we get

10y + x

→ 10(2) + 3

→ 20 + 3

→ 23

Therefore, the original number is 23.