Question

The sum of the digits of a two-digit number is 12. The number obtained by interchanging the digits exceeds the original number by 54. Find the original number.

Answer 1

Answer:

$\large\bold\red{39}$

Step-by-step explanation:

Let ,

the digit at ones place be 'x'

Then,

the digit at tens place will be (12-x)

Therefore,

Original Number = 10(12-x)+x = (120 -9x)

Now,

the digits are interchanged,

therefore,

the digit at ones place = (12-x)

and,

the digit at tens place = x

Then,

the new number = 10x + 12- x = (12+ 9x)

But,

according to Question,

we get,

$= > 12 + 9x = 120 - 9x + 54 \\ \\ = > 9x + 9x = 174 - 12 \\ \\ = 18x = 162 \\ \\ = > x = \frac{162}{18} \\ \\ = > x = 9$

Therefore,

12 - x = 12 - 9 = 3

Thus ,

original number = 120 - (9 ×9) = 120-81= 39

Hence,

39 is the required original Number.

Answer 2

Answer:

39

Step-by-step explanation:

Since The required Number is a two-digit number,so,we have to find itsones digit and its tens digit.

Let the digit at ones place be x

It is given that sum of digits of number is 12.

$\therefore$ The digit at tens place = 12-x

Thus,The Original Number =

$\implies \sf \: 10 \times (12 - x) + x$

$\implies \sf \: 120 - 10x + x$

$\sf \: \implies \: 120 - 9x$

On interchanging the digits of given number,the digit at ones place becomes (12-x) and digits at tens place becomes x.

$\therefore \: \sf New \: Number = 10x + (12 - x)$

$\sf \: \implies \: 9 x+ 12$

It is given That the new number exceeds the original number by 54

i.e New Number - Original Number = 54

$\implies \sf \: (9x + 12) - (120 - 9x) = 54$

$\implies \sf \: 9x + 12 - 120 + 9x = 54$

$\implies \sf \: 18x - 108 = 54$

$\implies \sf 18x = 54 + 108$

$\implies \sf \: 18x = 162$

$\sf \implies \: x = \dfrac{162}{18}$

$\boxed{\boxed{x\:= 9}}$

$\therefore$The digit at ones place = 9

$\therefore$ The digit at tens place = (12-9) = 3

$\sf \: Original \: Number = 39$