Question

la two digit number is four times the sum of its digits .if 36is added to number its digits are reversed then the number is

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Answer 1

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Let the digit in tens place be x and the digit in ones place be y .

Two digit number = 10x + y

Reversed number = 10y + x

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According to the first condition ,

      $\hookrightarrow\sf 10x+y =4(x+y)\\\\\hookrightarrow 10x+y = 4x+4y\\\\\hookrightarrow 10x-4x=4y-y\\\\\hookrightarrow 6x = 3y \\\\\hookrightarrow y = 2x \ \ \ \ \ \ \ \ \ \ .................(1)$

According to the second condition ,

   $\hookrightarrow \sf 10x+y+36 = 10y+x\\\\\hookrightarrow 10x-x+y-10y = -36\\\\\hookrightarrow9x-9y = -36 \\\\\hookrightarrow x-y = -4 \ \ \ \ \ \ \ \ ........(2) \\\\Substitute \ value \ of \ y \ in \ Eq(2) \ , \\\\\longrightarrow x-2x = -4 \\\\\longrightarrow -x=-4 \\\\\longrightarrow \bf x =4$

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Two digit number = 48

HOPE IT HELPS U ............. :)

Answer 2

Answer:

Let X be the digit on its ten's place and Y be the digit on its one's place.

The number is,

10 x + y

and when it reversed we would get ,

10 y+ x

According to the given condition,

10 x +y = 4 { x + y }

10 x + y = 4x + 4y

10x - 4x = 4y - y

6x = 3y

2x = y            [ eq.1]

According to the next condition,

10 x + y + 36 = 10 y + x

10 x - x + y - 10y =  - 36

9 x - 9y = -36

x-y = - 4         [ eq.2]

Substituting eq.1 on eq. 2,

4 = 2x -x

x = 4

Then y = 2x, ie, y = 8.

The number is 48 and the reversed number is 84.

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Hope this answer can help you dear...♥