Question

The sum of the digits of two digit is 18. If the digits are reversed the number is 126 more than the

original. Find the number.​

Answer 1

Answer:

I don't know the answer buddy 123 sorry

Answer 2

$\large{\underline{\boxed{\text{Given:}}}} </p><p>$

The sum of the digits of a two digit number = 18

If the digits are reversed the number = 126 more than the original number.

$\large{\underline{\boxed{\text{To find:}}}}</p><p>$

The original number

$\large{\underline{\boxed{\text{Solution:}}}}</p><p>$

Let the digit at tens place be x

and the digit at ones place be y

This implies

The original number = 10x + y

According to the question

$\textsf{x + y = 18}$

Now,

when the digits are reversed

Number = 10y + x

So,

According to the question

$\textsf{10y + x = 126 + (10x + y)}$

$\textsf{10y + x - (10x + y) = 126}$

$\textsf{10y + x - 10x - y = 126} \\ \\ \textsf{9y - 9x = 126} \\ \\ \textsf{9(y - x) = 126} \\ \\ \textsf{y - x} = \frac{126}{9}$

$\implies \textsf{y - x = 14}$

It can be written as

{ - (y -x = 14) }

$\textsf{x - y = - 14}$

Now we have,

$\textsf{x + y = 18} \\ \textsf{x - y = 14}$

Using Elimination Method

$\textsf{ x + {y} = 18} \\ \textsf{x - {y} = - 14}\\ \\\textsf{y will be cancelled}$

$\implies \textsf{2x = 4} \\ \\ \implies \textsf{x} = \frac{4}{2} \\ \\ \implies \boxed{ \textsf{ \green{x = 2}}}$

Putting the value of x in (x +y = 18)

$\implies \textsf{2+ y = 18} \\ \\ \implies \textsf{y = 18 - 2} \\ \\ \implies \boxed{ \textsf{ \green{y = 16}}}$

Putting the values to get original number

$\textsf{Original number = 10(2) + 16 } \\ \\ \textsf{Original number = 20 + 16 } \\ \\ \textsf{Original number } = \underline{\boxed{\red{36}}}$

Hope it helps you