Question

The digits of a 2-digit number differ by 6. Find the difference of the number and the number formed by reversing its digits.​

Answer 1

Answer:

54

Given:

Two digits numbet differ by 6

To find:

The difference of the number and the number formed after reversing

Solution:-

Let the two digits number be x and y

Difference between two digits=6

So,(x-y)=6

Now,Let the tens digits be 10x and unit digit be y (10x+y)

After reversing it will be (10y+x)

Now,According to the question

(10x+y)-(10y+x)

10x+y-10y-x

9x-9y

9(x-y)

Taking (x-y)=6. {Given above}

9(6)

9×6

54

-------------

The difference of the number and the number formed by reversing it's digits=54

Answer 2

$\bf{\huge{\underline{\boxed{\rm{\blue{Answer:}}}}}}$

Assumptions :-

Let the digits of a two digit number be x and y.

As per the first condition :-

The digits of a 2-digit number differ by 6,

x - y = 6 ---->1

As mentioned in the question : the digits of a 2-digit number, it means that the digit in the tens place is 10x and the digit in units place is y.

So the digit would be : 10x + y

We need to find : Number formed by reversing the digits and the difference of the number.

So the reverse of the digit : 10y + x

Let's hit up with the solution! :)

10x + y - (10y + x)

10x + y - 10y -x $\bf\underbrace{Multiplying\:terms \:by \:'-'}$

= 10x - x -10y + y

= 9x - 9y

= 9 ( x -y)

$\bf\underbrace{Taking\:9\:common}$

Now substitute the value of x-y from equation 1

= 9 (6)

= 54

$\bf{\large{\underline{\mathcal{\red{Number\: formed =54}}}}}$