Question

solve the problem with step​

Answer 1

Answer:

$\large \underline{\boxed{\textsf{Required number = 36}}}$

Step-by-step explanation:

$\large \underline{\underline{\textsf{Given that...}}}$

Sum of digits of a two-number is 9.The number obtained by interchanging the digits exceeds the given number by 27 . We need to find the original number..

$\large \underline{\underline{\textsf{Solution...}}}$

Now,

It's said that the number is a two-digit number

So let

$\textsf{The unit digit (ones digit ) be = x}$ and

$\textsf{Tens digit be = 10y}$

Therefore

The required number = 10y + x ------- (assumed form)

Now According to question

It's said that sum of that two numbers = 9 ( Note - It's number not the digits )

Therefore here

First number ( number at tense digit ) = y

Second number (number at one's digit ) = X

Thus we have

$\large \textsf{y + x = 9}$ ----------- eq (1)

Now it's also said that

The number obtained by interchanging the digits exceeds the original number by 27

That is when we change

$\mathsf{10y \rightarrow y}$

and

$\mathsf{ x \: \rightarrow \:10x}$

So we have equation

$\mathsf{10x + y = 10y + x + 27}$

$\implies \mathsf{9x - 9y = 27}$

$\implies \mathsf{9(x - y) = 27}$ (taking 9 as common)

$\implies \mathsf{x - y = 3}$

$\large \implies \mathsf{x = 3 + y }$ ---------- eq (2)

Now putting value of eq (2) in eq (1) we have ....

$\mathsf{(3+y) + y = 9}$

$\implies \mathsf{ 3 + 2y = 9}$

$\implies \mathsf{ 2y = 6}$

$\large \implies \mathsf{ y = 3}$

Now putting value of y = 3 in eq (2) we have

$\mathsf{x = 3 + (3)}$

$\large \implies \mathsf{ x = 6}$

Now by putting this values in the assumed form of number we have...

$\mathsf{10y + x}$

$\implies \mathsf{10(3) + 6}$

$\implies \mathsf{30 + 6 = 36}$

$\underline{\textbf{Required number is}}$

$\large \underline{\boxed{\mathsf{\bigstar \: 36 \: \bigstar}}}$

Answer 2

ANSWER:-

Given:

Sum of the digits of a two-digit number is 9.

The number obtained by interchanging the digits exceeds the given number by 27.

To find:

Find the original number.

Solution:

Let the unit's digit= x

The ten's digit = (9-x)

Therefore,

The original number;

=) 10(9-x)+x

=) 90 - 10x + x

=) 90 - 9x

On interchanging the digits, the new number;

=) 10x +(9 - x)

=) 10x + 9 -x

=) 9x + 9

According to the question:

[New number]= [original number]+27

=) 9x + 9= 90 -9x + 27

=) 9x + 9= 117 -9x

=) 9x + 9x = 117 -9

=) 18x = 108

=) x= 108/18

=) x = 6

Therefore,

The original number;

=) 90 -9x

=) 90 - 9(6)

=) 90 - 54

=) 36

Hence,

The original number is 36.

Hope it helps ☺️