Question

The difference between a 2-digit number and the number obtained by interchanging it's digits is 63. What is the difference between the digits of the number.

Answer 1

Answer:

A two digit number has two places, a unit digit, and a tens digit.

Let the tens digit be X/10. So without the unit digit, the number would be (X/10) * 10 = X.

let the unit digit be Y.

So the original number is : X + Y ………………………………….. (1)

I will explain this a little more. take a two digit number. for e.g. 27.

Nox X/10 is 2 and X is 20. Y is 7.

So X + Y = 20 + 7 = 27

Now, if you want to interchange the digits, the X will be at the units place and the Y will be at tens place.

So we will write it as : (Y * 10) + (X / 10)………………………….(2)

Now (Y * 10) + (X / 10) = (7 * 10) + (20 / 10) = 70 + 2 = 72.

Now, in your question, you said that the difference between the a digit number(i.e. X + Y) and the number formed by interchanging the digits(i.e. (Y * 10) + (X / 10)) is 63.

So therefore,

[X + Y] - [(Y * 10) + (X / 10)] = 63………………………………….(3)

[X - (X / 10)] + [Y - (Y * 10)] = 63

[9X / 10] + [9Y / 10] = 63

[9 * (X + Y)] / 10 = 63.

9 * (X + Y) = 63 * 10 = 630

X + Y = 630 / 9

X + Y = 70.

If you write it as:

X + Y = 70 + 0

X = 70, Y = 0

Now Substitute the same into third equation

[70 + 0] - [(0 * 10) + (70 / 10)] = 63

70 - [0 + 7] = 63

70 - 7 = 63

63 = 63.

So X and Y are verified.

Now answering your main question:

difference between the digits of the number = (X/10) - Y = (70/10) - 0 = 7 - 0 = 7.

So 7 is the answer