Question

in a two digit number,digit in units place is thrice the digit in yens place.If 54 is added to it digits are reversed.Find the number.​

Answer 1

GIVEN :-

• In a two digit , digit in unit's place is thrice the digit in ten's place ,

• If 54 is added to the number , the digits are reversed .

TO FIND :-

• The two digit number .

SOLUTION :-

 Let ,

  Digit in ten's place = x

  Digit in one's place = y

  Two digit number = 10x + y

  According to the first condition ,

  $\longrightarrow\sf y = 3x \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

  According to the second condition ,

  $\longrightarrow\sf 10x+y+54=10y+x \\\\\longrightarrow 10x-x+y-10y = -54 \\\\\longrightarrow 9x-9y = -54 \\\\\longrightarrow x-y = -6 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(2)$

 

 Substitute y = 3x in equation (2) ,

 $\longrightarrow\sf x-3x = -6 \\\\\longrightarrow -2x = -6 \\\\\longrightarrow \bf x = 3$

$\longrightarrow \sf y = 3x \\\\\longrightarrow \bf y = 9$

TWO DIGIT NUMBER = 39

Answer 2

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$\huge\bold\blue{\underline{\underline{{Given:-}}}}$

• In a two digit number,digit in units place is thrice the digit in tens place.

• If 54 is added to it digits are reversed.

$\huge\bold\purple{\underline{\underline{{To\:Find:-}}}}$

• Find the two digit number.

$\huge\bold\pink{\underline{\underline{{Solution:-}}}}$

• Let the digit in ten's place be x and the unit digit be y.

• The number will be represented as 10x + y.

$\sf\large{ ⟶ 10x + y + 54 = 10y + x}$

$\sf\large{but \: y = x2}$

So our equation turns to,

$\sf\large{⇝10x + x2 + 54 = 10 \times 2 + x}$

• if we rearrange equations by collecting like terms, we get a quardic equation in the form of :-

$\sf\large{⇝9x2 - 9x - 54 = 0}$

Divide through by 9,

$\sf\large{⇝x2 - x - 6 = 0}$

$\sf\large{⇝x2 + 2x - 3x - 6 = 0}$

$\sf\large{⇝x(x + 2) - 3(x + 2) = 0}$

$\sf\large{⇝(x + 2) - (x + 3) = 0}$

$\sf\large{⇝x + 2 = 0 \: or \: x - 3= 0}$

$\sf\large{⇝x = - 2 \: or \: x = 3}$

• Now x can't be negative... so x, the digit in the tens place = 3.

$\sf\large{⇝y = x2}$

$\sf\large{⇝y = {3}^{2} = 9 }$

So, The two digit number is 39.

To confirm,

$\sf\large{⟶ 39 + 54 = 93}$

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