Question

.
17. A two-digit number is four times the sum of its digits, and is also equal to twice the productof its digits. Find the number.
[CBSE (Delhi) 2004 C]​

Answer 1

Step-by-step explanation:

answer is above with explanation

Answer 2

Answer:

$\bigstar{\bold{The\:number=36}}$

Step-by-step explanation:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Two digit number = 4 times the sum of the digits
• Two digit number = 2 times the product of the digits

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• The number

$\Large{\underline{\underline{\bf{Solution:}}}}$

⇥ Let the unit's digit of the number be x

⇥ Let the ten's digit of the number be y

⇥ Hence,

   The number = 10y + x

⇥ By given

   The number = 4 (y + x)

   10y + x = 4y + 4x

   10y - 4y + x - 4x = 0

    6y = 3x

⇥ Dividing by 3

   x = 2y------(1)

⇥ Also by given,

   The number = 2 (x × y)

   10y + x = 2xy

⇥ Substitute the value of x from equation 1

   10y + 2y = 2 × 2 y × y

   12y = 4y²

   12 = 4y

   y = 12/4

   y = 3

⇥ Hence the ten's digit of the number is 3

⇥ Substitute the value of y in equation in 1

⇥ x = 2 × 3

   x = 6

⇥ Hence unit's digit of the number is 6

⇥ Hence,

   The number = 10y + x

   The number = 10 × 3 + 6

   The number = 36

   $\boxed{\bold{The\:number=36}}$

$\Large{\underline{\underline{\bf{Verification:}}}}$

⇥  10y + x = 4(y + x)

     10 × 3 + 6 = 4 (3 + 6)

     30 + 6 = 4 × 9

     36 = 36

⇥ 10y + x = 2 ( x × y )

    10 × 3 + 6 = 2 × 3 × 6

    30 + 6 = 6 × 6

    36 = 36

⇥ Hence verified.