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

Step-by-step explanation:

sum of digits that is x+y is equal to 9

here we get two equations

eq_1........x+y=9

10x+y-27=10y+x

10x+y-10y-x=27

-9y+9x=27

we are going to take 9 as common number

9(-y+x)=27

x-y=27/9

eq_2.........x-y=3

now we are going to subtract the two equations we have derived from the above question

x+y=9

x-y=3

x and x cancel so,

2y=12

y=12/2

y=6

we have y=6 now we are going to substitute the value of y in any one equation I am going to substitute it in eq_1

x+y=9

x+6=9

x=9-6

x=3

we got the answer ,it is

x=3,y=6

hope it helps

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