Question

A number consist of two digits whose sum is 9. If 27 is subtracted from the original number , its digits are interchanged. find the original numbers​

Answer 1

Answer :-

→ 63 .

Step-by-step explanation :-

Let the ones digit be x and the tens digit be y.

Now, A/Q,

°•° x + y = 9................(i)

Original number = 10y + x .

And, the number obtained on reversing the digits = 10x + y .

And,

°•°10y + x - 27 = 10x + y

==> 10y - y + x - 10x = 27

==> 9y - 9x = 27

==> 9 ( y - x ) = 27

==> y - x = 3...............(ii)

Now, add in eq. (i) and (ii), we get

x + y = 9

- x + y = 3

-....+......+

----------------

==> 2y = 12 .

•°• y = 6 .

Now, put the value of y = 6 in eq. (i) , we get

==> x + y = 9 .

==> x + 6 = 9 .

==> x = 9 - 6 .

\therefore∴ x = 3 .

Therefore, original Number = 10y + x .

= 10 ( 6 ) + 3 .

= 60 + 3 .

= 63.

Hence, The required number is 63.

Answer 2

$\huge\mathfrak\red{Answer :-}$

Let us assume, x and y are the two digits of the two-digit number

Therefore, the two-digit number = 10x + y and reversed number = 10y + x

Given:

→ x + y = 9 -------------1

also given:

10x + y - 27 = 10y + x

9x - 9y = 27

→ x - y = 3 --------------2

Adding equation 1 and equation 2

→ 2x = 12

→ x = 6

Therefore, y = 9 - x = 9 - 6 = 3

The two-digit number = 10x + y = 10*6 + 3 = 63

Answer - 63