Question

a 2 digit is such that the product of its digits is 20.if 9 is added to the number the digits interchange their places find the number. with all the steps

Answer 1

Let the digit at ten's place be x.
Let the digit at unit's place be y.
∴ Original Number = 10x + y

If the digits are interchanged, then New Number = 10y + x

The new number can be obtained by adding 9 to the original number.

∴ New Number = Original Number + 9
∴ 10y + x = 10x + y + 9
∴ 10y + x - 10x - y = 9
∴ 9y - 9x = 9
∴ y - x = 1 ----------------------(1)

Now, product of digits is 20.
∴ xy = 20
∴ x = 20/y

Substituting x = 20/y in (1)

∴ y - 20/y = 1
∴(y² - 20) / y = 1
∴y² - 20 = y
∴y² - y - 20 = 0
∴y² - 5y + 4y - 20 = 0
∴y(y-5)  -4(y-5) = 0
∴(y-5) (y-4) = 0
∴ y-5 = 0   or   y-4 = 0
∴ y = 5   or   y = 4

If y = 4
then y - x = 1
      ∴4 - x = 1
      ∴4 - 1 = x
      ∴ x = 3
 The number can be 34.     

If y = 5,
then y - x = 1
      ∴5 - x = 1
      ∴5 - 1 = x
      ∴x = 4
The number can also be 45.

Thus, the two digit number is 34 or 45.

Answer 2

it is 45.
4 x 5 = 20
45 + 9 = 54

i came to know the answer as soon as you told the digits interchange the places when 9 is added.