Question

The sum of the digits of a 2-digit number is 11. The number obtained by
interchanging the digits exceeds the original number by 27. Find the number,.

Tale me how the 10 is come​

Answer 1

Answer:

Number is 47

Step-by-step explanation:

Let the number be 10x+y

the digits are x and y

so equation generates as x+y=11--------(1)

by interchanging the digits we getthe no. as 10y+x

according to que.

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

=>9y-9x=27

=>9(y-x)=27

=>y-x=27/9

=>y-x=3

=>y=3+x-------(2)

putting value of (2) in (1)

=>x+(3+x)=11

=>2x+3=11

=>2x=8

=>x=4

.

.

.

putting value of x in (2)

y=3+4

=>y=7

so the no is 47..

Answer 2

Answer:

The number is 47

Step-by-step explanation:

Let,

Unit digit no. = x

Tens digit no. = 11 - x

Orignal Number =

10 (11 - x) + x

110 - 10x + x

110 - 9x

After interchanging digit no. obtained :

10 (x) + x (11 - x)

10x + 11 - x

10x - x + 11

9x + 11

According to question :

➙ (110 - 9x) + 27 = (9x + 11)

➙ 110 - 9x + 27 = 9x + 11

➙ 137 - 9x = 9x + 11

➙ -9x - 9x = 11 - 137

➙ - 18x = - 126

➙ $\sf{x \: = \: \dfrac{ - 126}{ - 18}}$

➙ x = 7

Unit digit no. = 7

Tens digit no. = 11 - x

➙ 11 - 7

➙ 4

Tens digit no. is 4

Therefore,

The number is 47