Question

A two digit number is such that the product of the digits is 12 when 36 is added to the this number the digits interchange their places determine the number

Answer 1

Answer:

Step-by-step explanation:

let the ones digit number be :x+10y

let the tens digit number be 10x+y

product of two number i.e x×y=12       equation 1

number is added to a number i.e original number :x+10y+36

Now

     10y+x+36=10x+y

     36=10x-x+10y-y

     36=9x-9y

      9(x-y)=36

        x-y=36÷9

        x-y=4

        x=4+y      equation 2

Now

     substituting the value of x in equation 1

x×y=12

(4+y)×y=12

4y+y²=12

y²+4y-12=0

y²+y(6-2)-12=0

y²+6y-2y-12=0

y(y-6)-2(y-6)=0

(y-2)(y-6)=0

Either

  y=2

Or

   y=-6

Now

substituting the value of y in the equation 2

x=4+y

x=4+2

x=6

NOW

   in original number i.e ones digit number

x+10y

6+10×2

6+20

26

Again

in tens digit number

10x+y

10×6+2

60+2

62

Therefore the original number is 26 and the interchange number is 62