Question

A two digit number is 3 more than 4 times the sum of its digit.If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits.find the number.

Answer 1

let the digits be x and y

the number = 4(x+y) + 3

ATQ

4(x+y) + 3 + 18 = 10y + x

4x + 4y + 21 = 10y + x

3x - 6y + 21 = 0

x - 2y + 7 = 0

x = 2y - 7

now

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

6x - 3y - 3 = 0

2x - y - 1 = 0

2(2y - 7 ) - y - 1 = 0

4y - 14 - y - 1 = 0

3y = 15

y = 5

now

x = 2y - 7 = 2(5)-7 = 3

the number is 35

Answer 2

Let y be the unit’s digit and x be the tens digit....so we have 10x+y=3+4(x+y)....10x+y=3+4x+4y.....6x-3y=3......2x-y=1
According to the second condition we have: 10x+y+18=10y+x.....9x-9y=-18......x-y=-2......subtract (x-y=-2) from (2x-y=1)....we get x=3....substituting the value of x in x-y=-2,we get y=5...hence the number is 35