A two digit number is four times the sum of its digits.If 18 is added to the number, the new number obtained is that by interchanging the digits of the original number.Find the number

Step1: 

A two digit number implies one number in the tens place and one number in the units/ ones place

                   Tens.     Units

                     10x        y

From above we consider the digit in the tens place as x and the digit in the units placa as y

Step 2 : 

A two digit number is four times the sum of its digits

                     10x + y = 4(x + y)

                     10x + y = 4x + 4y

                     10x - 4x + y - 4y = 0

                      6x - 3y = 0

                      3(2x - y) = 0

                         2x - y = 0/3

Hence Equation 1 is

                         2x - y = 0

If 18 is added to the number, the new number obtained is that by interchanging the digits of the original number

 

By interchanging the digits we get

                        Tens        Units

                          10y           x

Thus,

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

                         10x - x + y - 10y = -18

                          9x - 9y = -18

                           9(x - y = -2)

Thus Equation 2 is

                            x - y = -2

Step 3: Elemination of y

 

Subtracting both the Equations 

                      (2x - y = 0) - (x - y = -2)

                       2x - y - x + y = 2

                                 x = 2

Step 4: substituting the value of x in Equation 1

                          2x - y = 0

                          2x = y 

                          2(2) = y

                           y = 4

Thus the number is 

                   10x + y= 10(2) + 4 = 20 + 4 = 24