Question

3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
found that the resulting new number is greater than the original number by 27. What
is the two-digit number?
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Answer 1

Let the two digit number be 10x + y, then;

x+y = 9

or, x = 9 - y ......(1)

And, 10y+x = 10x+y + 27

or, 9y - 9x = 27

or, 9(y-x) = 27

or, y - x = 3

or, x = y-3 ......(2)

Substituting (1) and (2), we get;

9-y = y - 3

or, - 2y = - 12

or, y = 6

Then, x = y - 3 = 3

Thus the two digit number = 10x + y = 30 + 6 = 36

HOPE THIS COULD HELP!!!

Answer 2

Answer :-

→ 36 .

Step-by-step explanation :-

Let the ten's digit of the required number be x .

And, the unit's digit be y .

Then,

°•° x + y = 9 ........ (1) .

Required number = ( 10x + y ) .

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

•°• 10y + x = 27 + 10x + y .

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

==> 9x - 9y = -27 .

==> 9( x - y ) = -27 .

==> x - y = -27/9 .

•°• x - y = -3 .........(2) .

On substracting equation (1) and (2), we get

x + y = 9 .

x - y = -3 .

-..+.....+

__________

==> 2y = 12 .

==> y = 12/2 .

$\therefore$ y = 6 .

Putting the value of y in equation (1) , we get

==> x + 6 = 9 .

==> x = 9 - 6 .

$\therefore$ x = 3 .

Therefore, the required number = 10x + y .

= 10 × 3 + 6 .

= 30 + 6 .

= 36 .

Hence, it is solved .