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.

the answer is 47.explain

Answer 1

Step-by-step explanation:

let the digit in unit place be x

let the digit in tens place be y

the number is written as 10x + y

interchanging the digits it becomes 10y + x

which is 27 more than the original number

sum of the two digits x + y = 11

$10x + y + 27 = 10y + x \\ 10x + y - (10y + x) = - 27 \\ 10x + y - 10y - x = - 27 \\ 9x - 9y = - 27 \\ 9(x - y) = - 27 \\ x - y = \frac{ - 27}{9} \\ x - y = - 3$

x + y = 11

x - y = -3

adding the above equation we get

2x = 8

x = 8/2

x = 4

substitute x in x + y = 11

x + y = 11

4 + y = 11

y = 11 - 4

y = 7

the required number is 10x + y

= 10(4) + 7

= 40 + 7

= 47

hope you get your answer

Answer 2

Step-by-step explanation:

here's your answer.........