Question

the sum of the digits of a two-digit number is 17 the new number formed by receiving the digital is greater than the original number by 9 find the original number ​

Answer 1

$\large\sf\underline{Assuming}$

• Tens digit of a number be A .

• One's digit of a number be B .

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$\large\sf\underline{Number\:formed}$

• Original Number = 10A + B

• Reversed Number = 10B + A

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$\large\sf\underline{Given}$

• The sum of the digits of a two digit number is 17 .

$\sf\:A + B = 17$

$\sf➞\:A= 17-B--(i)$

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• The new number formed by reversing the digits is greater than the original number by 9 .

$\sf➞\:10A + B + 9 = 10B + A --(ii)$

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$\large\sf\underline{Solution}$

In equation (ii) ,

$\sf\:10A + B + 9 = 10B + A$

Substituting the value of A from equation (ii) :

$\sf➻\:10(17-B)+ B + 9 = 10B + (17-B)$

$\sf➻\:170-10B+ B + 9 = 10B + 17-B$

$\sf➻\:-10B-10B+ B+B=17 -9-170$

$\sf➻\:-20B+ 2B= -162$

$\sf➻\:-18B= -162$

$\sf➻\:18B= 162$

$\sf➻\:B= \frac{162}{18}$

${\sf{{\pink{➲\:B=9}}}}$

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Now substituting the value of B in equation (i) :

$\sf\:A= 17-B$

$\sf➻\:A= 17-9$

${\sf{{\pink{➲\:A=8}}}}$

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Now the original number would be :

$\sf\:Original\: Number = 10A + B$

$\sf\:Original\: Number = 10(8) + 9$

$\sf\:Original\: Number =80 + 9$

${\small{\fcolorbox{blacl}{white}{\fcolorbox{black}{red}{\bf{\color{black}{➲\:Original\: Number =89}}}}}}$

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!! Hope it helps !!

Answer 2

$\large\sf\underline{CORRECT\:QUESTION:-}$

Q: The sum of the digits of a two-digit number is 17. The new number formed by reversing the digits is greater than the original number by 9. Find the original number.

$\large\sf\underline{Answer:-}$

• The original number = 89

$\large\sf\underline{Step\:by\:step\:Explaination:-}$

Let us assume:

Tens digit of a number be A.

Ones digit of a number be B.

Number formed:

Original number = 10A + B

Reversed number = 10B + A

$\large\sf\underline{Given\:That:-}$

The sum of the digits of a two-digit number is 17.

⇒ A + B = 17

⇒ A = 17 - B _____(i)

The new number formed by reversing the digits is greater than the original number by 9.

⇒ 10A + B + 9 = 10B + A _____(ii)

$\large\sf\underline{To\:find:-}$

• The original number.

Finding the values of A and B:

In equation (ii).

⇒ 10A + B + 9 = 10B + A

Substituting the value of A from eqⁿ (i).

⇒ 10(17 - B) + B + 9 = 10B + (17 - B)

⇒ 170 - 10B + B + 9 = 10B + 17 - B

⇒ - 10B + B - 10B + B = 17 - 170 - 9

⇒ - 18B = - 162

Minus sign cancelled both sides.

⇒ 18B = 162

⇒ B = 162/18

⇒ B = 9

Now, In equation (i).

⇒ A = 17 - B

Substituting the value of B.

⇒ A = 17 - 9

⇒ A = 8

Finding the original number:

⇒ Original number = 10A + B

Substituting the values of A and B.

⇒ Original number = 10(8) + 9

⇒ Original number = 80 + 9

⇒ Original number = 89

${\small{\fcolorbox{blacl}{white}{\fcolorbox{black}{red}{\bf{\color{black}{➲\:Original\: Number =89}}}}}}$