Question

The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54,find the original number.

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Answer 1

QUESTION:-

The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54, find the original number.

SOLUTION:-

Let the digits be x and y, so the number will be = (10x+y), on reversing the digits, the new number will be = (10y+x)

According to the question we can write as x + y=12 and also we can write as 10y+x-10x-y=54

Which implies 9y-9x=54

y-x=54/9

y-x=6

y=6+x

Now on substituting this in x + y=12 we get

x+6+x=12

2x+6=12

2x=12-6

x=6/2=3

Now ,

y=6+x=6+3=9

So the number is 39.

To check: digit sum=3+9=12

Reversing the digit numbers becomes 93 and 93-39=54.

Hence Verified.

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Answer 2

Correct Question-:

• The sum of the digits of a two digit number is 12. If the new number formed by reversing the digits is greater than the original number by 54 . Find the original number.

AnswEr-:

• $\underline{\boxed{\star{\sf{\blue{  Two\:Digit\:Number\: = 39.}}}}}$

EXPLANATION-:

• $\frak{Given \:\: -:} \begin{cases} \sf{ The \:sum\: of\: the \:digits \:of \:a\: two \:digit \:number \:is \:12.} & \\\\ \sf{The\: new\: number\: formed \:by\: reversing\: the \:digits\: is \:greater\: than \:the \:original\: number\: by \:54 .\: }\end{cases}$
• $\frak{To \:Find\: -:} \begin{cases} \sf{ The\: original \:number\:.}\end{cases}$

Solution -:

• Let the numbers of two digit number be x and y .
• Then,
• The two digit number is (10x + y )
• It is given that ,
• The sum of the digits of a two digit number is 12.

Then ,

• $\implies{\sf{\large { x + y = 12 }}}$ ___________[1]

Then,

• It is also given that ,

• The new number formed by reversing the digits is greater than the original number by 54 .

So,

• 10y + x - ( 10x + y )=54
• 9y - 9x = 54
• 9y - 9x = 54 9(y -x ) = 54
• 9y - 9x = 54 9(y -x ) = 54y - x = 54/9
• $\implies{\sf{\large { y - x = 6 }}}$_____________[2]

Add -: Equation 1 + Equation 2

Here,

• Equation 1 = x + y = 12
• Equation 2 = y - x = 6

Then ,

• x + y + y - x = 12 +6
• x + y + y - x = 18
• y + y = 18
• 2y = = 18
• y = 18/2
• y = 9

Therefore ,

• y = 9

Now -:

• Putting " y = 9" in Equation 1 .
• Equation 1 = x + y = 12
• $\frak{Putting \:y=9\: -:} \begin{cases} \sf{ x +9 = 12 .} & \\\\ \sf{x = 12-9 .\: } & \\\\ \sf{ x =3 } \end{cases}$

Therefore,

• X = 3

Now ,

• The two digit number is (10x + y )
• Here -:
• X = 3
• Y = 9

Now ,

• 10(3) + 9
• 30 + 9
• 39

Hence ,

• $\underline{\boxed{\star{\sf{\blue{  Two\:Digit\:Number\: = 39.}}}}}$

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♤ Verification ♤

• Putting " x = 3" and " y = 9" in Equation 1 .

Here,

• Equation 1 = x + y = 12

Now ,

• 3 + 9 = 12
• 12 = 12

Therefore,

• LHS = RHS
• Hence , Verified.

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