Question

Sum of digits of a two digit number is 11 . if the digits are interchanged the number so got is 27 more than it . find the number

Answer 1

Answer:

74

Step-by-step explanation:

Let’s represent the tens digit with ‘a,” and the ones digit with ‘b.’

The value of this number is 10a + b; this number is 27 more than the number formed by the same digits in the other order, so 10a + b = 10b + a + 27.

The digit sum is 11; a + b=11, or b = 11 - a.

10a + b = 10b + a + 27

10a + (11 - a) = 10(11 - a) + a + 27

10a + 11 - a = 110 - 10a + a + 27

9a + 11 = 110 - 9a + 27

9a + 11 = 137 - 9a

18a + 11 = 137

18a = 126

a = 126/18

a = 7

b = 11 - 7 = 4

So the original number is 74.

The sum of the digits is 7+4=11.

And if you reverse the digits you get 47; 47 + 27 = 74

Answer 2

$\sf{\huge{\underline{\green{Given :-}}}}$

• The Sum of digits of a two digit number is 11 .

• The digits are interchanged the number so got is 27 more than it .

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The original number.

$\sf{\huge{\underline{\green{Answer :-}}}}$

Let the number at unit be x,

According to the question,

The Sum of digits of a two digit number is 11 .

x + y = 11

➝ y = ( 11 - x ) ------(a)

The numbers = 10y + x

➝ 10 ( 11 - x ) + x

➝ 110 - 10x + x

➝ 110 - 9x

Interchanging the numbers ,

10x + y

➝ 10x + ( 11 - x )

➝ 10x + 11 - x

➝ 9x + 11

The digits are interchanged the number so got is 27 more than it .

11 + 9x = 110 – 9x + 27

➝ 9x + 9x = 110 – 11 + 27

➝ 18x = 126

➝ x = 126/18

➝ x = 7

putting in equation (a)

➝ y = ( 11 - 7 )

➝ y = 4

The original number is 47.