Question

If the sum of a two digit number is 9. If the digits are interchanged the answer is 27 more than the original number. Find the number.

Answer 1

Let the digits be x and 9 - x

The number in the unit's place is x

The number in the ten's place is 9 - x

Then the number is 10 ( 9 - x ) + x

                               = 90 - `10 x + x

                               = 90 - 9 x

If the digits are interchanged the number becomes 10 x + 9 - x

                                                                                    = 9 x + 9

Given :

9 x + 9 - 27 = 90 - 9 x

==> 18 x = 90 + 18

==> 18 x = 108

==> x = 108 / 18

==> x = 6

The original number = 90 - 9 x

                                  = 90 - 9 × 6

                                  = 90 - 54

                                  = 36

The number is 36

Hope it helps

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Answer 2

•○●Heya..!!

•○● Here is your answer ●○•

Let the unit place digit be x & ten place digit digit be y

then number = 10y + x

A. T. Q

Case 1 : Sum of digit = 9
x + y = 9
x = 9-y [ equation 1 ]

Case 2 : Interchanging the places
New number = 10x + y

New number = 27 + original number
10x + y = 27 + 10y + x
10x - x + y - 10y = 27
9x - 9y = 27
9(x - y) = 27
x - y = 27
x - y = 27/9
x - y = 3

From equation 1

9 - y - y = 3
9 - 2y = 3
-2y = 3 - 9
-2y = -6 [ Minus cancel by Minus ]
y = 6/2
y = 3

From Equation 1

x = 9 - y
x = 9 - 3
x = 6

Then, the number = 10y + x
= 10 × 3 + 6
= 30 + 6
= 36

Hence, 36 is the two-digit number

☆ HOPE IT HELPS..!! ☺☺