Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reversed. Find the number​

Answer 1

Answer:

63

Step-by-step explanation:

Let the number be 10x + y

x + y = 9 -------------------------- 1

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

By re arranging the equation we get ,

10 x + x + y - 10 y = 27

11x - 9y = 27 --------------------- 2

we know from the first equation that x = 9-y

we substitute the value of x in the second equation

11 ( 9-y ) - 9y = 27

99 - 11y - 9y = 27

99 - 20 y = 27

20 y = 99 - 27

        = 72

y = 72 / 20

  = 18 / 5

x + y = 27

x + 18 / 5 = 27

x = 27 - 18/5

  = 117 / 5

10 x + y = 10 × 117 / 5 + 18 / 5

            = 63

hope it helped :)

Answer 2

Answer:

36 or 63 can be the number

Step-by-step explanation:

Assuming

x as tens digit

y as ones digit

Their sum :

x + y = 9 ..... (i)

Number formed :

10x + y

Interchanging the digits :

10y + x

According to the question :

➡ (10x + y) - (10y + x) = 27

➡ 9x - 9y = 27

➡ 9(x - y) = 27

➡ x - y = 27/9

➡ x - y = 3 ..... (ii)

Subtracting both the equation :

$\bf \: x + y = 9 \\ { \underline{ \bf{x - y = 3}}} \\ \implies \bf \: 2x = 6 \\ \implies \bf \: x = 3$

Substituting the value of x in equation (i) :

➡ x + y = 9

➡ 3 + y = 9

➡ y = 6

Hence

The number can be 10x + y

or, 10(3) + 6

or, 36 either 63