The sum of the digits of a two digit number is 11 the number got by interchanging the digits is 27 more than the original number. What is this number ?

Let the digit in one's place be y and digit at ten's place be x.

Sum of the digits = 11

⟶ x + y = 11

⟶ x = 11 - y -- equation (1).

And,

The number formed by reversing the digits is 27 more than the original number.

⟶ Reversed number = Original number + 27

reversed number = 10y + x.

⟶ 10y + x = 10x + y + 27

⟶ 10y + x - 10x - y = 27

⟶ 9y - 9x = 27

Substitute the value x from equation (1).

⟶ 9y - 9(11 - y) = 27

⟶ 9y - 99 + 9y = 27

⟶ 18y = 27 + 99

⟶ 18y = 126

⟶ y = 126/18

⟶ y = 7

Substitute the value of y in equation (1).

⟶ x = 11 - 7

⟶ x = 4

The number = 10(4) + 7 = 40 + 7 = 47.

∴ The required two digit number is 47.

I hope it will help you.

Regards.

picture below

d is correct

step-by-step explanation: