Question

The product of the digits of a two digit number is 24. If it's units digit exceeds twice it's ten digit by 2.find the number

Answer 1

let the ten digit be x
unit digit=y
2x+2=y
(2x+2)x=24
2x^2 + 2x -24=0
x^2 + x - 12=0
(x-3)(x+4)=0
x=3

y number=2(3)+2=8
Number=30+8=38

Answer 2

Step-by-step explanation:

Let , unit digit = x and Tens digit = y , So our number will be = 10 y + x

From first condition we get

xy = 24 , So

y = 24/x --- ( 1 )

And , from second condition we get

x = 2 y + 2 , Substitute value from equation 1 and get

⇒x = 2 ( 24x ) + 2

⇒x = 48 + 2 x/x

⇒x 2 = 48 + 2 x

⇒x2 - 2 x - 48 = 0 , Now we use splitting the middle therm method and get

⇒ x2 - 8 x + 6 x - 48 = 0

⇒x ( x - 8 ) + 6 ( x - 8 ) = 0

⇒( x + 6 ) ( x - 8 ) = 0 , So

x = - 6 and 8 , But we assume x as our unit digit of two digit number and one digit can't be negative , So we neglect x = - 6 and get

x = 8 , Substitute that value in equation 1 and get

y = 248 = 3

Therefore,

Our number = 10 ( 3 ) + 8 = 30 + 8 = 38 ( Ans )