Question

A two digit number is four times the sum of its digits and twice the product of its digits. Find the number.
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Answer 1

${\bold {\huge {\underline {\mathfrak {\green{Answer:}}}}}}$

$\boxed{\red{\bold{Given:}}}$

Their are 2 digits and the no. is four times the sum of its digits and twice the product .

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$\boxed{\red{\bold{Find:}}}$

The two numbers = ?

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$\boxed{\red{\bold{Solution:}}}$

Let the numbers be x and y

${\underline {\blue {ATQ ,}}}$

10x + y = the number

${\underline {\blue{A\: two\: digit\: number\: is\: 4 \:times\: the\: sum \:of \:its \:digits}}}$

= 10x + y = 4(x+y)

= 10x + y = 4x + 4y

= 10x - 4x = 4y - y

= 6x = 3y

${\underline {\blue{Divide\: both \:sides\: by\: 3}}}$

2x = y

10x + y = 2xy

Replace y with 2x

10x + 2x = 2x × 2x

12x =${4x}^{2}$

Divide both sides with 4x

3 = x

${\underline {\blue{Putting \: 3\: in \: place\: of \: x}}}$

y = 2x = 2 × 3 = 6

$\boxed{\red{\bold{Then \: the \: number \: is \: 36}}}$

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Answer 2

Hello!

Here is the answer for your question!

Question:-  A two digit number is four times the sum of its digits and twice the product of its digits. Find the number.

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Answer:-

         Let the digit at tens place be x and units place be y respectively,

         given,

                   10x + y = 4 (x+y) -------------------(1)

            and, 10x + y = 2 (xy)  ------------------(2)

from (1),

             10x + y = 4x + 4y

             6x = 3y

             y = 2x ------------------------(3)

substituting value of y in (2)

             10x + 2x = 2 (2x²)

             12x = 4x²

             x² = 3x

            x = 3

substituting value of x in (3)

          y = 2 × 3

         y = 6

hence, the two digit number is 36

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Hope this helped you with your doubt :)