# 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

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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.

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.