Question

A number consists of two digits whose product is 18 if 27 added to the number the digits interchange their places find the number

Answer 1

Answer:

36

Step-by-step explanation:

let the number be xy where X is tens digit and y is unit digit then

X*y = 18

X = 18/y

now

10x + y +27 = 10y + X

9x -9y +27 = 0

X -y +3 = 0

(18/y) -y +3 = 0

18 - y^2 + 3y = 0

y^2 -3y -18 = 0

y^2 -6y + 3y -18 = 0

y ( y-6) +3(y-6) = 0

( y-6) ( y+3) = 0

y = 6 or -3 ( neglecting -3)

y = 6

X = 3

so the number is 36

Answer 2

Answer:

36

Step-by-step explanation:

Let the unit digit be 'y' and the tens digit be 'x'.  Thus, the number be 10x + y.

Product of digit = xy = 18  ⇒ x = 18/y

If 27 is added to the number, the digits interchange their places. And the new number becomes 10y + x.

⇒ (10x + y) + 27 = 10y + x

⇒ 27 = 9y - 9x

⇒ 3 = y - x

⇒ 3 = y - (18/y)        {from above}

⇒ 3y = y² - 18

⇒ y² - 3y - 18 = 0

⇒ y² - 6y + 3y - 18 = 0

⇒ (y + 3)(y - 6) = 0

  As y can't be -ve, y = 6.

Thus , x = 18/y = 18/6 = 3

∴ Required number = xy = 36