Question

The sum of a digit of the two digit number is 9.If 45 is added to the number.The digit are interchanged.find the number

Answer 1

Answer:

27

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Answer 2

Let the -

• ten's digit be M
• one's digit be N

The sum of a two-digit number is 9. (Means, the sum of one's and ten's digit number is 9)

According to question,

=> $\sf{M\:+\:N\:=\:9}$

=> $\sf{M\:=\:9\:-\:N}$ ....(1)

If 45 is added to the number.

Number = 10M + N

If we add 45 to number i.e. (10M + N), then the digits interchanged their place.

We have -

• Original number = 10M + N

On interchanging place, N takes place of M and vice versa.

• Revered number = 10N + M

According to question,

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

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

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

Take 9 common from both sides

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

=> $\sf{M\:-\:N\:=\:-\:5}$ ...(2)

Substitute value of (eq 1) in (eq 2)

=> $\sf{9\:-\:N\:-\:N\:=\:-\:5}$

=> $\sf{-\:2N\:=\:-\:14}$

=> $\sf{N\:=\:7}$

Substitute value of N in (eq 1)

=> $\sf{M\:=\:9\:-\:7}$

=> $\sf{M\:=\:2}$

$\therefore$ Number = 10M + N

From the above calculations, we have M = 2 and N = 7

So,

=> $\sf{10(2)\:+\:7}$

=> $\sf{20\:+\:7}$

=> $\sf{27}$

Answer :-

Original number = 27

_____________________

Verification :

We have -

• M = ten's digit number = 2
• N = one's digit number = 7

substitute value of M and N in (eq 1)

→ 2 = 9 - 7

→ 2 = 2