Question

the digit at tens place of atwo digit no is 2more than twice the digit at unit place if the product of digits is 24 find the two no​

Answer 1

Hi.

Good Question and Keep Progressing.

Here is your answer---

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Let the digits at unit place be y and at tens place be x.

Thus, Number = 10x + y

According to the question,

      x = 2 + 2y -------------------------eq(i)

Also, xy = 24 -----------------------------eq(ii)

Putting eq(i) in eq(ii),

(2 + 2y)y = 24

 2y + 2y^2 - 24 = 0

   2y^2 + 2y - 24 = 0

     y^2 + y - 12 = 0

Splitting The middle Term,

 

     y^2 + 4y - 3y - 12 = 0

     y(y + 4) - 3(y + 4) = 0

              (y+4)(y - 3) = 0

By Zero Product Rule,

 y + 4 = 0                          y - 3 =0

 y = -4                                y = 3

For y = -4 in eq(i),

 x = 2 + 2( -4)

 x = 2 - 8

 x = -6

For, y=3 in eq(i)

x = 2 + 2(3)

x = 2 + 6

 x = 8

For x = 8 and y= 3,

Number = 10(8) + 3

             = 80 + 3

             = 83

For x = -6 and y = -4

Number = 10(-6) + (-4)

             = -60 -4

             = -64

Thus, Two - digits number is 83 or -64.

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Hope it helps.