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.
Answers
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
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