Question

- When the digits of two-digit numbers
are reversed, the number increases by
27, the sum of such two-digit numbers
is​

Answer 1

Answer:

The sum of such two-digit numbers could be 5 or 7 or 9 or 11 or 13 or 15.  

Step-by-step explanation:

Let the first digit of the two-digit number be “x” and the second digit be “y”.

Therefore,

The two-digit no. = (10x + y)

On reversing, the two-digit number becomes = (10y + x)

According to the equation we can write the equation as,

(10x + y) + 27 = (10y + x)

Or, 10y – y – 10x – x = 27

Or, 9y – 9x = 27

Or, y – x = 27/9 = 3

Or, y – x = 3 ….. (i)

For the equation (i) above let’s assume some value of x so that the we can calculate the value for y and the final result we get as a two-digit number.

Case 1: x=1

∴y – 1 = 3

or, y = 4

∴two-digit no. = 14

Case 2: x=2

∴y – 2 = 3

or, y = 5

∴two-digit no. = 25

Case 3: x=3

∴y – 3 = 3

or, y = 6

∴two-digit no. = 36

Case 4: x=4

∴y – 4 = 3

or, y = 7

∴two-digit no. = 47

Case 5: x=5

∴y – 5 = 3

or, y = 8

∴two-digit no. = 58

Case 6: x=6

∴y – 6 = 3

or, y = 9

∴two-digit no. = 69

From each of the above cases, we could have the two-digits as 14 or 25 or 36 or 47 or 58 or 69.

And, the sum of the digits of each of the two-digit number that we will get are (1+4=)5 or (2+5=)7 or (3+6=)9 or (4+7=)11 or (5+8=)11 or (6+9=)15.

Answer 2

Answer:

Number = 36

Step-by-step explanation:

Complete Question is :

When the digits of two-digit numbers  are reversed, the number increases by  27 the sum of such two-digit numbers  is​ 9

Find number

Let say Number = XY

Value of number = 10X + Y

Reversed Number = YX

Value of Reversed number = 10 Y + X

given that the number increases by  27

=> 10Y + X = 10X + Y + 27

=> 9(Y - X) = 27

=> Y - X = 3

   Y  + X = 9

Adding Both 2Y = 12

=> Y = 6

& X = 3

Hence Number = 36