Question

the difference between 2 digit number and the number obtained by interchanging its digits is 63. what is difference between the digits of the number?

Answer 1

Let the two digit number be $10x+y,$ assuming $x>y,$ and so the number obtained by interchanging the digits will be $10y+x.$

We're asked to find the difference between the digits of the numbers, i.e., $x-y.$

Given that the difference between these two numbers is 63.

$\longrightarrow(10x+y)-(10y+x)=63$

$\longrightarrow10x+y-10y-x=63$

$\longrightarrow9x-9y=63$

$\longrightarrow9(x-y)=63$

$\longrightarrow x-y=\dfrac{63}{9}$

$\longrightarrow\underline{\underline{x-y=7}}$

Therefore, the difference of the digits is 7.

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Result:-

If the difference between a two digit number and the number obtained by interchanging the digits is $D,$ then the difference of the digits will be $\dfrac{D}{9}.$

According to the question,

$\longrightarrow D=63$

Hence the answer is,

$\longrightarrow\underline{\underline{\dfrac{D}{9}=7}}$

Answer 2

Answer:

x - y = 7

Step-by-step explanation:

Assume that the ten's digit be x and one's digit be y.

So, original number is 10x + y.

As per given condition, the difference between two digit number and the number obtained by interchanging it's digits is 63.

As the original number is 10x + y. Then it's interchange will be 10y + x.

Let's say that original number is bigger then the smaller one.

Therefore,

Bigger number - Smaller number = 63

10x + y - (10y + x) = 63

10x + y - 10y - x = 63

9x - 9y = 63

Take 9 as common,

9(x - y) = 9(7)

x - y = 7

Hence, the difference between the two digit number and the number obtained by interchanging its digits is 7.