Question

A number consisting of two digits exceeds 4 times the sum of the digits by 3. If 27 is added to the number, the place of the number are interchanged, find the number

Answer 1

Answer:

let the tens unit be x and ones unit be y

so

10x + y = 4(x + y) + 3

10x + y = 4x + 4y +3

6x - 3y = 3

2x - y = 1                   ------1

10x + y + 27 = 10y + x

9x - 9y + 27 = 0

x - y + 3 = 0            ----------2

Subtracting both the equations

2x - y - x + y = 1 + 3

x = 4

Substituting in 1

8 - y = 1

y = 7

number = 10x + y = 47

Answer 2

let the num be 10x+y

10x+y=4(x+y)+3

=>10x+y=4x+4y+3

=>6x-3y=3

10x+y+27=10y+x

=>9x-9y=27

=>x-y=3

=>6x-6y=18

=>6x-6y-6x+3y=18-3

calculate yourself I'm too lazy to write