a two digit number is such that the sum of its digits is 11. the number is 27 greater tha the number obtained by interchanging the digits. find the number

Answer 1

a = first digit

b = second digit

Two digit number is formed when ten's digit which is multiplied by 10 and add to unit place digit is multiplied by 1.

In this case your number is 10 a + b

The number obtained by interchanging the digits is 10 b - a

The sum of digits is 11 mean:

a + b = 11

The number is 27 greater than the number obtained by interchanging the digits mean:

10 a + b = 10 b + a + 27

Now:

10 a + b = 10 b + a + 27

Subtract b to both sides

10 a + b - b = 10 b + a + 27 - b

10 a = 9 b + a + 27

Subtract a to both sides

10 a - a = 9 b + a + 27 - a

9 a = 9 b + 27

Divide both sides by 9

a = b + 3

Replace this in equation:

a + b = 11

b + 3 + b = 11

2 b + 3 = 11

Subtract 3 to both sides

2 b + 3 - 3 = 11 - 3

2 b = 8

Divide both sides by 2

b = 4

a = b + 3 = 4 + 3 = 7

a = 7

Your number is 74

Proof:

a + b = 7 + 4 = 11

74 = 47 + 27