Question

in a two digit number the digit in unit place is twice the digit in tenth place if 27 is added to it digits are inverse find the number​

Answer 1

Given :-

• In a two digit number digit in units place is twice the digit in the tens place.
• If 27 is added to the number its digits are reversed.

Solution :-

 Let ,

  ➣  Digit in tens place = x

  ➣  Digit in ones place = 2x

  ➟ Required number = 10x + 2x = 12x

  ➟ Number obtained by interchanging the digits ,

                                      = 10(2x) + x  =21x

   According to the question ,

       $\hookrightarrow \sf 12x+27 = 21x\\\\\hookrightarrow 21x - 12x = 27\\\\\hookrightarrow 9x = 27 \\\\\hookrightarrow \bf x = 3$

   

  ➤ Required number = 36

 

Answer 2

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$\huge\red{\underline{{\bf Question : }}}$

• In a two digit number the digit in unit place is twice the digit in tenth place if 27 is added to it digits are inverse find the number.

$\huge\red{\underline{{\bf Answer : }}}$

$\bf\large{\underline\blue{Given:-}}$

• In a two digit number the digit in unit place is twice the digit in tenth place if 27 is added to it digits are inverse.

$\bf\large{\underline\green{To\: Find:-}}$

• Find the number.

$\bf\large{\underline\orange{Solution:-}}$

• Let x denote the digit in the tenth place and y denote the digit in unit place.

• So, the number may be written as x y 10 + in the expanded form. (just like 35= 10(3) +5)

• When the digits are reversed, x becomes the digit in unit place and y becomes the digit in the tenth place.

• The changed number, in the expanded form is 10 y + x.

▪️According to the first condition, we have,

$\sf\large\blue{⇝y = 2x \: which \: is \: written \: as \: }$

$\sf\large\blue{⇝2x - y = 0 ....... (1) }$

▪️Also, by second condition, we have,

$\sf\large\pink{⇝(10 + x) - (10x + y) = 27}$

▪️That is,

$\sf\large\pink{ ⇝- 9x + 9y = 27 ⟼ - x + y = 3.......(2)}$

• Adding equations (1) and (2), we get x= 3.

• Substituting x 3 = in the equation (2), we get y = 6.

• Thus, the given number is,

${\boxed{{\bf{(3×10)+6=36}}}}$

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