# A number consists of two digits whose product is 18. When 27 is subtracted from the number,the digits change their places. Find the number.

2
by dweejareddy

63

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by dweejareddy

63

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Let the digits be x and y

so given xy = 18

⇒y = 18/x ................(i)

so the number is 10x + y

so now given

10x + y - 27 = 10y + x

⇒9x - 9y = 27

⇒ x - y = 3 ..... (ii)

substituting (i) in (ii)

⇒ x - 18/x = 3

⇒x² - 3x - 18 = 0

⇒ x² - 6x + 3x - 18 = 0

⇒ x(x - 6) + 3(x - 6) = 0

⇒(x + 3)(x - 6) = 0

so x = - 3, 6

so x cannot be negative

so x = 6

so y = 18/x ⇒ y = 18/6 = 3

so the number is 10x + y

= 10 × 6 + 3

= 63__ANSWER__

so given xy = 18

⇒y = 18/x ................(i)

so the number is 10x + y

so now given

10x + y - 27 = 10y + x

⇒9x - 9y = 27

⇒ x - y = 3 ..... (ii)

substituting (i) in (ii)

⇒ x - 18/x = 3

⇒x² - 3x - 18 = 0

⇒ x² - 6x + 3x - 18 = 0

⇒ x(x - 6) + 3(x - 6) = 0

⇒(x + 3)(x - 6) = 0

so x = - 3, 6

so x cannot be negative

so x = 6

so y = 18/x ⇒ y = 18/6 = 3

so the number is 10x + y

= 10 × 6 + 3

= 63