Question

The sum of the digits of a two digit number is 11. When the digits are interchanged, the new number formed is 27 less than the original number. Find the original number​

Answer 1

Answer:  Let the number =

xy. Then x+y = 11. It’s value = 10x+y

The reversed number yx and it’s value = 10y+x

Difference between the two numbers = 10y+x-10x-y = 9y-9x = 27

x+y=11 and y-x = 3 so y=7 and x=4

The given number = 47 or 74 … QED

hi buddy hopes this helps you and others who are in need.......................

Answer 2

$\huge\blue{solution}$

The original number is 74.

$\huge\boxed{\fcolorbox{red}{yellow}{explanation}}$

Let the two digit number be 10a + b

number obtained after reversing the digits.

10b + a.

______________________________________

ATQ

a + b = 11 [equation 1]

______________________________________

ATP

10a + b - (10b + a) = 27

10a + b - 10b - a = 27

9a - 9b = 27

9(a - b) = 27

a - b = 27/3

a - b = 3 [equation 2]

______________________________________

Putting the two equations together we get,

a + b = 11

a - b = 3

--------------

2a = 14

a = 7.

______________________________________

putting the value in the equation 1, We get.

7 + b = 11

b = 4.

______________________________________$\huge\sf\bold\pink{hope\: it\: helps\: you}$${\huge{\overbrace{\underbrace{\green{thanks}}}}}$