Question

The sum digits of the two-digit number is 17. The new number obtained by reversing the digits is 9 more than the original number find the number.​

Answer 1

AnsWer :

X = 8 and y= 9

i.e., 89.

Solution :

Case 1.

The Sum of digits of two digit number is 17.

Let,

The Unit place be y and tenth place be x.

Original Number is 10x + y.

• X + Y = 17.

$\rule{200}2$

Case 2.

The new number is obtaining by reserving the digits is 9 more than the original number.

• 10x+y +9= 10y+x.

$\rule{200}2$

Now, We have Two equation.

$\bullet \: \: \tt x + y = 17. - - - (1)$

$\bullet \: \: \tt10x + y + 9 = 10y + x. - - - (2)$

Taking equation, 2.

$\tt \implies9x - 9y = - 9.$

9 Common both Sides,

$\tt \implies \: x - y = - 1 - - - (3)$

Now,

$\begin{tabular}{1-1} x + y = 17. &\\ x - y = -1.& \\ \cline{1-1} 2x = 16.& \\ \cline{1-1} \end {tabular}$

By equation 3 and 4 adding, we get.

$\implies \tt 2x = 16.$

$\implies \tt x = 8.$

Putting the value of x in equation 3.

$\implies \tt x - y = - 1.$

$\implies \tt 8 - y = - 1.$

$\implies \tt y = 9.$

$\tt \bigstar \: Original \: number\begin{cases} \sf{x = 8.} \\ \sf{y = 9.} \end{cases}$

$\tt \bigstar \: its \: digits\begin{cases} \sf{ \tt89.} \end{cases}$

Therefore, the value of the number 89.

Answer 2

Anwer:-

89

Given:-

Sum of two digit number is 17.

New number obtained by reversing the digits is 9 more than the number

To find:

The number

Solution:-

Let the ten's digit number be 10x

and one's digit number be Y

The Number= 10x+y

10x+y=17 (Given) ........i)

On reversing the numbers

10y+x

New number is exceed by 9

so, 10y+x+9

Now solving both equations

$(10x + y) - (10y + x + 9) = 0$

$10x + y - 10y - x = - 9$

$9x - 9y = - 9$

$9(x - y) = - 9$

$x - y = - 1 \: \: \: \: \: ....ii)$

Adding i) and ii)

$x + y + x - y = 17 + ( - 1)$

$2x = 16$

$x = 8$

Subtracting i) and ii)

$x + y - (x - y) = 17 - ( - 1)$

$x + y - x + y = 18$

$2y = 18$

$y = 9$

________________________

Hence; The number= 10x+y

=10×8+9

=80+9

=89