Question

the difference between a number and the number obtained by interchanging its digits with 45 what is the difference between the digits of that number?​

Answer 1

Answer :

$\underline{\boxed{\sf{M\:-\:N\:=\:5}}}$

Step-by-step explanation :

Let the ten's digit be M and one's digit number be N.

$\implies\:\sf{Number\:=\:10M\:+\:N}$

If we interchange the digits then M takes the place of N and N of M.

In short, M becomes one's digit and N becomes ten's digit.

$\implies\:\sf{Number\:=\:10N\:+\:M}$

The difference between a number and the number obtained by interchanging its digits with 45.

i.e.

Original number - Interchanged number = 45

$\longrightarrow\:\sf{10M+N\:-\:(10N+M)\:=\:45}$

$\longrightarrow\:\sf{10M\:+\:N\:-\:10N\:-\:M\:=\:45}$

$\longrightarrow\:\sf{9M\:-\:9N\:=\:45}$

Take 9 as common

$\longrightarrow\:\sf{9(M\:-\:N)\:=\:9(5)}$

9 throughout cancel

$\longrightarrow\:\sf{M\:-\:N\:=\:5}$

Therefore, the difference between the digits is 5.

Answer 2

Correct Question :-- The difference between a Two digit number and the number obtained by interchanging its digits is 45 what is the difference between the digits of that number ?

Solution :---

Let the Two digit number be 10x+y . where x is at Ten's place and y is at unit place .

When we interchange the digits it becomes, = 10y+x .

A/q , now,

→ 10x+y - (10y+x) = 45

→ 10x + y - 10y - x = 45

→ 10x - x + y -10y = 45

→ 9x -9y = 45

→ 9(x-y) = 45

Dividing both sides by 9 , we get,

→ (x -y) = 5 . (Ans).

So, The difference b/w the digits will be 5 in this case...

→ Possible cases are (x,y) : (6,1) (7,2) (8,3) (9,4) ...