Question

the difference between a 2 digit no.and the no. obtained by interchanging it's digit is 63 . what is the difference between the no.
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Answer 1

Answer:

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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

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